ENERGY LOSS IN PIPES, Darcy- weicbach formula, Chezy's formula, minor losses in pipe

MECHANICAL TIPS AND STUDY MATERIAL

When ever there is flow of fluid in pipes there will be resistance which add to energy loss. For our study, we have classified the losses in two section, these are

• Major losses in pipe
• Minor losses in pipe

Major losses are mostly due to friction which is basically experienced by 

• Surface of pipe and layer of fluid flowing over it.
• Subsequent layer of fluids creating resistance to neighboring layer.

It can be calculated by Darcy - weisbach formula and Chezy's formula.

Darcy - weisbach formula

Where,

hf = head loss

L = length of pipe

d = diameter of pipe

f = coefficient of friction

V = mean velocity of flow

Chezy's formula.

Where,

hf = loss of head due to friction

P = perimeter of pipe

A = area of cross section of pipe

L = length of pipe

V = mean velocity of flow

Minor losses in energy can arise from several factors. Some of them are as under.

• Any obstruction in pipe
• Bending in pipe
• Unanticipated contraction
• Unexpected expansion
• Fittings etc in pipe

Also losses occurs at entrance and exit of pipes which are unavoidable. All such losses accounts for loss of head of fluid in pipe. These are minor losses as compared to frictional loss which can be neglected for long pipes but are taken into account when we deal with short pipes.

Loss of head due to sudden enlargement and contraction

Consider a pipe of diameter D1 (smaller) with sudden enlargement having diameter D2 (larger). The liquid moving from smaller to larger diameter pipe experiences sudden change in boundry an is not able to follow the abrupt change in boundary resulting into formation of turbulence or eddies. This adds to the loss of head in the pipe.


When fluid is flowing in larger diameter pipe and suddenly experiences change in diameter (reduced diameter of flow), the flow goes on decreasing upto section C - C and then suddenly increases causing loss of head. Then section C - C is also known as vena-contracta.

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METHOD FOR DETERMINATION OF CO- EFFICIENT OF VISCOSITY

MECHANICAL TIPS AND STUDY MATERIAL

various experimental methods are used to determine coefficient of viscosity of a liquid. These are as under.

1) Rotating cylinder method
2) Orifice type viscometer
3) Capillary tube method
4) Resistance by falling sphere method

Rotating cylinder method

Look at the figure, you will find two concentric cylinders with inner cylinder having radii R1 and outer cylinder with radii R2. The space between the two cylinders is filled with liquid whoseviscosity is to be determined. Keeping the inner cylinder stationary, outer cylinder is rotated at constant angular speed (w).  The inner cylinder is held stationary by the help of torsional spring. The torque acting on inner cylinder is equal and opposite in nature to that acting in outer cylinder. The torsional spring with the help of dial and pointer measures the magnitude of torque acting in inner cylinder.

How is torque transmitted from inner to outer cylinder?

Torque acts on the outer cylinder the layer of liquid which is in contact with the inner cylinder's outer surface experiences torque. This torque is transmitted to subsequent layers of liquid and finally to outer cylinder.

Let w = angular speed of outer cylinder

Coefficient of viscosity is given by

                   2(R2 - R1)CT
            ---------------------------------------------
         Π R1^2[4HCR2 + R1^2(R2 - R 1)

WhereR1 = inner radii
R2 = outer radii
C = Clarence at bottom
H = height of liquid


Orifice viscometer

In your engineering course you will come across instruments like Saybolt and redwood viscometer, these are orifice type viscometers.


The liquid whose viscosity it to be calculated is allowed to flow through a capillary tube. The time taken by certain quantity of liquid to flow the tube is noted down and it is compared with coefficient of viscosity of a known liquid.

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RECIPROCATING PUMPS

MECHANICAL TIPS AND STUDY MATERIAL

Pumps are the machines capable of converting mechanical energy into hydraulic energy (pressure energy). In reciprocating pumps liquid is sucked in a cylinder in which piston is reciprocating. This action of piston exerts thrust on liquid and increases its hydraulic energy. Such type of pumps are called as reciprocating pumps.

Construction of reciprocating pumps - Single acting

The main components of such a pump are:-
1) Suction pipe and valve
2) Cylinder - piston arrangement with connecting rod and crank
3) Delivery pipe and valve

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As shown in the figure crank is connected to connecting rod, through which piston (closely fitted to cylinder) is connected. The crank is rotated by the means of electric motor. When crank rotates, connecting rod provides reciprocating action to the piston. 

Suction pipe and delivery pipe with their valves are connected to cylinder. The valve is provided so that only one way motion is possible and fluid does not return to sump. The suction pipe allows entry of liquid from sump to the cylinder only and Similarly delivery valve allows liquid flow from cylinder to delivery pipe only.

OPERATION

When motor is powered, it rotates the crank which allows the piston to reciprocate (to and fro motion) in the cylinder. Initially suppose the piston is in extreme left end. On rotation of crank, it starts moving right. Due to this partial vacuum in the cylinder is created. But the surface of the liquid in sump is experiencing atmospheric pressure which is greater than that inside the cylinder. Thus liquid is forced to move in suction pipe and enters the cylinder by passing through suction valve. When piston starts moving from extreme right end to leftwards, then pressure on the liquid is higher then atmospheric pressure. This closes the suction valve and opens delivery valve and liquid is forced out of delivery pipe. Thus weight can be lifted through this pressurized liquid. 


Discharge and Work done by reciprocating pump

Discharge (Q) can be calculated by formula 

                                   Q = A X L X (N/60)

Where A is cross section area of piston or cylinder 

L is length of stroke
N is rpm of crank and (N/60) means revolution per second.

WORK DONE

Work done (W) by reciprocating pump per second can be given by equation


                    W = Density x Gravity x LAN/60

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HYDRAULIC CRANE WITH CONSTRUCTION, WORKING AND NEAT IMAGE

MECHANICAL TIPS AND STUDY MATERIAL

This device has wide application in warehouses, dock slide, work shops etc. It is used for transferring or lifting bulk loads.
The main components are 

1) Mast
2) Jib
3) Tie
4) Cylinder - Ram arrangement
5) Guide pulley
6) Jigger

Construction and working

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Mast is the vertical structure from which jib and tie are attached. The mast can revolve around the vertical axis. The jib can be lowered or raised as per the requirement of crane.

The jigger which consists of sliding ram fitted in cylinder arrangement provides the necessary action for lifting/lowering the load. The lower end of cylinder- ram arrangement is provided with inlet for high pressure water.This end has fixed pulley block which in turn is fixed with cylinder jigger. The upper end of ram is connected to movable pulley which can move up and down.

The wire rope is provided through which load is attached which is to be lowered or lifted. This wire rope passes over the guide pulley And is fixed to movable pulley which in turn is attached to sliding ram.

Lifting of load

When the load is to be lifted, the high pressure water is admitted to cylinder of jigger which forces the ram to move upwards. As the ram moves upward the movable pully attached with it also moves upward. This increases tension in wire and distance between two pully blocks also increases. This action lifts the load. Similarly for lowering the load, water is allowed out of the cylinder, thus the ram comes down with movable pully and load is lowered.

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Hydraulic accumulator

MECHANICAL TIPS AND STUDY MATERIAL


As the name implies, this device is capable of storing energy of liquid in form of pressure. This pressure energy is utilized suddenly or in intermittent manner in machine parts like hydraulic cranes or lifts. 

Construction

It consists of of large vertical hollow cylinder in which ram can slide through. The ram can slide in up - down direction. The ram is fitted with bulk load at its top end. A pressurized water inlet at the bottom end of cylinder is provided. Through this inlet high pressure water enters the cylinder which forces the ram to move upward against the bulk weight. 

On the other side of cylinder, there is outlet pipe which is connected to machine like hydraulic lift or cranes. when the machine does not require water pressure, the ram keeps on moving upward because of inlet liquid pressure. At the topmost point of ram, enough pressure energy is accumulated in the accumulator.

When machine requires large energy, the accumulator supplies the liquid under high pressure and ram starts moving downward.

There is a expression to determine the maximum capacity of hydraulic accumulator. This is nothing but the maximum amount of hydraulic energy that can be stored in accumulator. This is simply known as capacity of accumulator.

The work done in lifting the ram = Capacity of accumulator
Let, 
A = area of sliding ram
W = bulk load on the ram and also weight of ram
P = Pressure of liquid from inlet
L = Lift of the ram by pressure "P"

Now,                        W = P X A   ---------------------- (1)
Work done to lift the ram = W X L  --------------------(2)
There fore on substituting equation (1) in equation (2) we get,

                                 work done = P x A x L
Also we know that Area x Length = Volume 
therefore, 

CAPACITY OF ACCUMULATOR = P x ( A x L ) = P x Volume

This relation will be helpful in solving numerical problems. One of such type is provided below for your practice.

Q > The water is supplied at pressure of 18 N/Cm^2 to an accumulator. The ram has diameter of 2 meter. If the total ram lift is 6 meter, the find:
1 ) Accumulator capacity
2 ) Total weight on the ram

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HYDRAULIC LIFTS - FLUID DEVICE

MECHANICAL TIPS AND STUDY MATERIAL
Hydraulic lift

It is a hydraulic device which is capable or transporting goods or passenger through small distance or from one floor to another in a building. These are mainly of two types

• Direct acting hydraulic lift
• Suspended hydraulic lifts

Direct acting lifts

It is very simple in construction. It consists of a vertical hollow cylinder. A ram which can slide is fitted inside the cylinder. The ram has a cage fitted on its top end. This cage is nothing but the platform on which goods can be placed or people can stand. A liquid under pressure can be forced form bottom which strikes the ram. As such the ram moves in upward direction and reaches the desired height. If the cage is to be moved in downward direction, the liquid under pressure is allowed to move out of cylinder. This allows the ram to move down and hence cage comes down.

• Suspended hydraulic lift

It is has slight alterations but the principle of working is similar to direct acting hydraulic lift. As shown in figure, it has cage suspended by the wire or rope. As discussed earlier, cage is the platform on  which people stand or goods are kept.

There are two pulley blocks ( fixed and movable ) out of which ram is connected to movable block. A wire or rope connects the pulley, passes over guide pulley to the cage.

Operation

When liquid under high pressure is injected into the cylinder, it strikes the ram and it is forced to move left. The movable pulley connected to it also moves left side. This increases tension in the wire and the cage is lifted upwards to desired height. When it is to be lowered, the pressurized liquid is forced out of cylinder and ram along with the pulley move right and the tension in strings is reduced. Hence the cage comes downwards.

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GEAR WHEEL PUMP - HYDRAULIC DEVICE

MECHANICAL TIPS AND STUDY MATERIAL

Gear Wheel Pump

The meshing of two rotating gears provide the pumping action. The construction of gear pump is very simple. One of the gear is connected to driving shaft, which rotates as the shaft supplies power. This gear is connected to another gear called driven gear. These two gears provide meshing. The case surrounds the gear arrangement and the space between gear and casing is filled with oil which is to be pumped. The oil in suction side is carried to delivery side via gears. The meshing of gears .

Does not allow the flow from inlet to outlet directly. The oil is carried forward from suction side through outer tip/edge of gears.

Oil pumped per second or discharge of oil can be calculated by formula

                   (2Lan× N/60)m^3
Where

L = axial length of teeth,
N = speed of theeth in rpm,
a = area between teeth,
n = number of teeth on each gear,

Note - we devide by 60 to obtain discharge in seconds.

Advantage

The flow of fluid is uniform and continuous

Uses

• For cooling water
• Provides pressurized oil for lubricating motor parts.

Note- Actual discharge is always less than theoretical.

Volumetric efficiency = Actual discharge / theoretical discharge

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FLUID DEVICES - HYDRAULIC PRESS, AIR LIFT PUMP, GEAR WHEEL PUMP

MECHANICAL TIPS AND STUDY MATERIAL

FLUID DEVICES

These are devices in which transmission of power takes  place by fluid as medium. The fluid medium may be liquid ( oil, water ) or gas. Based on fluid mechanics and fluid statics various devices are as under.

1 ) The hydraulic press
2 ) Air lift pump
3 ) Hydraulic ram
4 ) Gear wheel pump
5 ) Hydraulic accumulator

There are other devices also but in this section we will study in detail the above mentioned devices.

THE HYDRAULIC PRESS

It is device which is used to carry or lift heavy weight with small application of force. Intensity of pressure in static fluid is transmitted equally in every direction. This statement is pascal's law which applies in the case of hydraulic press.

The hydraulic press has two cylinders of different diameter. One diameter has plunger and other with ram. The plunger is one through which force is applied and ram is one which weight is kept which is to be lifted.

The section in between is filled with fluid through which pressure is transmitted.

When force "F" is applied on the plunger in download direction. This force is applied on fluid which in turn applied on ram, which moves the heavy weight placed above it.

Let,
W = weight to be lifted
F = Force applied on plunger
P = pressure produced by force "F".
A = area of ram
a = area of plunger

                       P =( F/a )•A

The ratio of weight lifted to force applied is called as mechanical advantage.
                       M.A = ( W/F )

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HYDRAULIC TURBINES

MECHANICAL TIPS AND STUDY MATERIAL

HYDRAULIC TURBINES

These are the devices that convert the hydraulic/water energy into mechanical energy to generate mechanical work. These devices are reverse of pumps which we have studied in previous article where mechanical energy is utilized to generate water energy. The water energy may be in the form of potential or kinetic energy. Potential energy is static water source like dam or large reservoir and kinetic energy can be found in running water.

CLASSIFICATION OF HYDRAULIC TURBINES

      Direction of fluid flow

      Specific speed

      Water action on the blades

1.      Direction of fluid flow:

      Axial flow

      Radial flow

      Tangential flow

      Mixed flow

Axial flow water turbines:

In such turbines, the direction of flow of water is parallel to the axis of rotation of runner. Such type of turbines is propeller and Kaplan turbine.

Radial flow turbines:

As the name implies, the water enters the turbine in radial direction and the flow of water is perpendicular to the axis of rotation of runner. Flows are of two types namely 1) inward flow 2) outward flow.

In inward flow, water enters the turbine from periphery and directed towards the runner and leaves from inner periphery. Whereas in Outward flow type machines the water enters from inner periphery, goes pass the runner and exits through outer periphery. It is just the reverse case of inward flow type machine.

Tangential flow turbines:

Such flow is categorized by flow of water in tangential direction to the rotation of runner. Consider the figure of Pelton wheel as shown in the above figure which represents the tangential action of water jet on the turbine blades.

Mixed flow type turbines:

Mixed flow type is combination of radial and axial flow actions of water. In such flow type, the water enters the turbine radially inwards (outer periphery) and passes over the runner and then it exits axially (parallel to axis of rotation of runner). Its application is Deriaz turbine.

2.  SPECIFIC SPEED

      Low specific speed

      Medium specific speed

      High specific speed

Low specific speed turbines employ large head and low discharge. The head may be in range of 200 meter – 1800 meter. Example is pelton wheel.  Medium specific speed turbines have head 50 meter – 200 meter. These have moderate head and discharge. Example is Francis turbine. High specific speed turbines have small head but with large discharge. The head may maximum go up to 50 m. Examples is Kaplan turbine.

3. ACTION OF WATER ON THE BLADES OF TURBINE:

      Impulse

      Reaction

Impulse action of water:

In such machines only kinetic energy is available at the inlet of turbine for generating power or transforming energy and pressure at the inlet and outlet is the same. Given below is the impulse action of water on the blades.

Reaction type turbines:

In addition to kinetic energy present at the inlet of machine, the fluid also has potential energy for power generation and energy transformation. Example is Parson’s turbine.

The various types of efficiencies encountered in hydraulic turbines are:

      Mechanical efficiency

      Hydraulic efficiency

      Volumetric efficiency

      Overall efficiency

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CASING OF CENTRIFUGAL PUMP, ITS TYPES AND PRIMING OF TURBINES

MECHANICAL TIPS AND STUDY MATERIAL

CASING OF CENTRIFUGAL PUMP

As we know casing surrounds the impeller and guides the water and also raises the static head. These are designed in such a way that the kinetic energy of water at the outlet of impeller is converted into pressure energy. Mainly three types of casing are used for centrifugal pumps.

Ø  Volute casing

Ø  Vortex casing

Ø  Diffuser casing

We will discuss all the three casing in detail.

1)      VOLUTE CASING – Spiral type casing

In such casing the area of flow increases gradually from inlet (throat) to output (delivery pipe). As the area of flow increases gradually the velocity decreases and pressure energy increases.

The only demerit of such casing is formation of eddies where lot of energy is wasted. But on the whole the efficiency of pump can be increased slightly.

2)      VORTEX CASING – Circular casing

This is simple arrangement with circular chamber between the impeller and casing. The prime advantage of such construction is that there are negligible eddy losses. Hence energy loss is negligible and efficiency increases. So we can say that vortex casing is better than volute casing.

3)      DIFFUSER CASING

These types of casing consist of additional guide blades in-between casing and impeller. These guide blades are mounted on a ring type structure called diffuser. When the water from impeller enters to the guide blade and its velocity is further reduced as the water flows through increased area of flow. Due to reduced velocity of water the pressure energy is increased. It is to be noted here that the efficiency of the diffuser cased pump are greater than the volute and vortex casing pump.

PRIMING – ITS IMPORTANCE

A pump is primed properly before one starts it for operation. It is process of removing air from the suction pipe, impeller and the casing.

Now let’s see how priming is done. To remove the air present, the suction pipe, casing and the delivery pipe is completely filled with water. This removes the air out of the pump.

At this point you must ask a question that – Since head generated by the pump is independent of fluid, WHY CAN’T WE USE AIR AS WORKING FLUID AND WHY PRIMING IS NECESSARY?

The answer is very simple. If we use air as working fluid the head generated is in terms of meters of air. When we use water as working fluid the head generated is in terms of meters of water. As we know that density of air is very less as compared to water, the head produced with air as working fluid will be far negligible than water  as working fluid. Hence we remove air from the pump part as it may not be sufficient to suck the water from the sump and will reduce the efficiency of the pump. To remove such difficulty priming is done

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PUMPS, MULTISTAGE PUMPS, LOSSES IN PUMP

MECHANICAL TIPS AND STUDY MATERIAL

PUMPS

These are devices which are efficient in conversion of mechanical energy into hydraulic energy or also called pressure energy. Basically categorized on fluid flow direction as under:-

• Axial flow pump
• Centrifugal pump
• Mixed flow pump

Let’s start with centrifugal pump in detail.

Centrifugal pump is the name derived because the head generated by the pump is result of centrifugal action. The construction of such pump consists of:-

• Impeller
• Casing

Impeller is mounted on the shaft and it lifts the water from low level to required high level. This is done by forced vortex motion which generates dynamic pressure. Due to generation of dynamic pressure the water leaving the impeller has high velocity. This high velocity water then enters static blades called casing. We use Bronze made impeller to handle small capacity but for large water and corrosive situation we use stainless steel and aluminium-bronze impellers. Given below is the figure of impeller.

Casing is the guide ways that directs the fluid flow and also add in raising the static head. Static head is nothing but the vertical distance between the liquid level in sump (lower level) and the delivery tank (high level). These are blades which are fixed around the impeller to act like diffuser and increase the static pressure.

MULTISTAGE PUMPS

Multistage pumps are required when high discharge or high head is required. First of all we have to know what multistage pump is. A multistage pump consists of two or more impellers which may be connected in series or parallel.

Ø  To develop high head – SERIES CONNECTION

When high head is required then number of impellers are connected in series such that water enters into first impeller through suction pipe and the pressure increases and then this increased pressure water enters into second impeller where pressure adds up more. The discharge is same in both the impeller but the head is increased which is greater than either of the one.

Ø  To develop high discharge – PARALLEL CONNECTION

When we require high discharge or flow we connect impellers in parallel. Each pump sucks water from sump and delivers it to common pipe. The common pipe receives large amount of water which is result of sum of water received by each of the pump. Hence the discharge increases. All the pump works under same head in this case.

PUMP LOSSES 

Mainly there are three losses that are encountered in centrifugal pump:-

Ø  Mechanical losses

Ø  Hydraulic losses

Ø  Leakage

Mechanical losses occur mainly due to friction. These are:-

Ø  Friction on the main bearing glands.

Ø  Friction between rotor and the fluid.

Hydraulic losses occur due to many reasons. These are:-

Ø  Loss in suction and delivery pipes.

Ø  Friction loss in casing and vanes and impeller.

Ø  At entry and exit of impeller shock and eddy current losses occur.

Leakage is integral part of centrifugal pumps. There is always some amount of leakages or water slip out and never passes through the delivery pipe due to which some part of energy is also wasted. This is called leakage loss.

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BERNOULLI'S THEOREM AND ITS APPLICATION-PITOT TUBE AND VENTURIMETER

BERNOULLI'S THEOREM AND APPLICATION

In steady flow of fluid, the Bernoulli principle state that at any point of time the sum of all form of energy along the streamline is same. It means that the kinetic energy, potential energy and the internal energy of fluid is constant.

Consider a case of fluid flow,where the speed of fluid increases. With the increase in speed it gains kinetic energy and dynamic head. But at the same time there is decrease in potential energy, internal energy and also static head.

Observe the above figure carefully, the fluid enters through section"1" of venturimeter and moves out through section "2". As you can see inlet section is of larger diameter and and outlet section is smaller in diameter.

At section "1" the fluid has high pressure and less velocity. But as it enters section "2" the pressure energy gets converted to kinetic energy and the fluid gains speed. The difference in pressure is depicted by difference in manometric head "h" (AS SHOWN IN FIGURE). Hence one form of energy is converted to another. This is basic idea of BERNOULLI'S principle.

NOTE -Bernoulli's principle is valid for incompressible fluid only

Bernoulli's equation is given by:-

Where,

p1  - pressure at section 1

v1 -  velocity at section 1

z1 - height of fluid at section 1.

P2  - Pressure at section 2

V2  -  velocity at section 2

Z2  - height at section 2

g - acceleration due to gravity.

p - density of fluid at all point.

APPLICATION OF BERNOULLI'S THEOREM:-

PITOT TUBE

INVENTED BY-HENRI PITOT(18th century)

A pitot tube is a instrument which is used to measure pressure by determining fluid flow velocity. In the modern times it is widely used in industrial application for measuring air speed an in aircraft to measure speed of air.

A pitot tube has a pointing tip which is exposed directly to fluid flow. The flowing fluid in tube enters the tube, since the other end is closed and connected to pressure measuring device, the fluid is brought to rest (static). The pressure at this moment is known as pitot pressure.

PITOT PRESSURE = STATIC PRESSURE + DYNAMIC PRESSURE

Static pressure is obtained from static ports available in pitot tube and dynamic pressure is obtained by fixing a diaphragm in pitot tube. When fluid flows there is diaphragm present between the static and stagnation side. The movement of diaphragm determines the dynamic pressure.

Once the dynamic pressure is known the speed can be easily determined by the means of mechanical levers.

APPLICATION:-

• Determine mach number, speed.
• Determine both static and dynamic pressure.

VENTURIMETER

A venturimeter is a device that helps to create velocity head by restricting the pressure through the restricted area. The venturimeter was first coined by an Italian physicist Gaiovanni Battista Venturi in 18th century. In order to maintain continuity the fluid must flow with increase in speed through the reduced cross section in order to balance the pressure. The decrease in pressure or pressure drop determines the flow rate. The tube has length varying from 100 mm to 1000 mm and the inlet portion has angle of around 30 degree and exist section has angle of about 5 degree. Its use is avoided if the flow of fluid has Reynold's number less than 1.5*10^5.

Note- In venturimeter density of the fluid is assumed to be constant even though its pressure changes.

Numerical questions 

1) Velocity of discharge is given by relation V = QA, where Q is discharge and A is area.

1) The state is correct
2) The statement is incorrect
3) Can't be justified.

2) The total head is equal to _______________.

1) Pressure head - Velocity head
2) Velocity head - Pressure head
3) Pressure head + Velocity head
4) Pressure head * Velocity head

3) According to Bernaulli's theorem, which statement holds good?

1) Pressure energy gets converted to kinetic energy.
2) Kinetic energy gets converted to pressure energy.
3) No energy transfer takes place.

4) Bernaulli's theorem is applied only for?

1) Real fluid
2) Ideal fluid
3) Viscous fluid
4) All of them

5) According to Bernaulli's theorem, Pressure head + Velocity head + Height = ____________?

1) Variable
2) Constant

6) In Bernaulli's theorem, frictional losses are neglected.

1) True
2) False

7) The unit of discharge of flow is given by?

1) m^2/sec
2) m^3/sec
3) m^3/sec^2
4) m^2/sec^2

Be first to answer these questions via comment.
Thankyou.

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