hydraulics lab

Hydraulics Lab (ECIV 3122) Islamic University Gaza (IUG)

Instructors : Dr. Khalil M. Alastal Eng. Mohammed Y. Mousa 1

Experiment (7): Investigation of Bernoulli's theorem

Introduction:

The flow of a fluid has to conform with a number of scientific principles in particular the

conservation of mass and the conservation of energy. The first of these when applied to a liquid

flowing through a conduit requires that for steady flow the velocity will be inversely proportional

to the flow area. The second requires that if the velocity increases then the pressure must decrease.

Bernoulli's apparatus demonstrates both of these principles and can also be used to examine the

onset of turbulence in an accelerating fluid stream.

Both Bernoulli's equation and the continuity equation are essential analytical tools required for the

analysis of most problems in the subject of mechanics of fluids.

Purpose:

To verify Bernoulli's equation by demonstrating the relationship between pressure head and

kinetic head.

Apparatus:

1. Bernoulli's apparatus (Figure 1).

2. Hydraulic bench.

Figure 1: Bernoulli's apparatus



Bernoulli's apparatus consists essentially of a two dimensional rectangular section convergent

divergent duct designed to fit between constant head inlet tank and variable head outlet tank. An

eleven tube static pressure manometer bank is attached to the convergent divergent duct. The

differential head across the test section can be varied from zero up to a maximum of 450mm. The

test section, which is manufactured from acrylic sheet, is illustrated in figure below

Figure 2: Test section of Bernoulli's apparatus

The convergent divergent duct is symmetrical about the center line with a flat horizontal upper

surface into which the eleven static pressure tappings are drilled. The lower surface is at an angle of

4 29'. The width of the channel is 635 mm. The height of the channel at entry and exit is 19525

mm and the height at the throat is 635 mm. The static tappings are at a pitch of 25 mm distributed

about the centre and therefore about the throat. The flow area at each tapping is tabulated below

the dimensions which are shown in figure 3.



Figure 3: Duct dimensions

Tapping number

1 2 3 4 5 6 7 8 9 10 11

Flow area

(mm2) 102.56 90.11 77.66 65.22 52.77 40.32 52.77 65.22 77.66 90.11 102.56

Equipment set up:

Position the inlet head tank and the variable head outlet tank on the mounting studs provided on

the hydraulic bench working surface and connect the Bernoulli apparatus between them using the

union connections. Connect the bench feed hose to the inlet head tank and attach an overflow hose

to the overflow outlet of the inlet head tank.

Prepare the equipment to the following specification :

Inlet : Constant head inlet tank with overflow extension fitted.

Test section : Bernoulli's apparatus.

Exit : Variable head outlet tank.

Manometer: Insert a sheet of graph paper 440mm high by 325mm wide behind the manometer

tubes to provide an easy method of obtaining a record of the results.



Theory:

1. Bernoulli's theorem

Bernoulli's equation is applicable to the steady flow of an incompressible and inviscid fluid.

Bernoulli's equation shows that the sum of the three quantities :

are constant. Therefore the three terms must be interchangeable so that, for example, if in a

horizontal system the velocity head is increased then the pressure head must decrease

2. Loss of head due to friction

If the fluid is not inviscid then there will be a small loss of head due to friction within the fluid and

between the fluid and the walls of the passage. Bernoulli's equation can then be modified by the

inclusion of the frictional head loss

Where Bernoulli's equation has been written in the integrated form and has been applied between

the upstream section 1 and the downstream section 2.

Since the passage is horizontal . At two positions of equal area the two velocities will be

equal thus the equation reduces to

Most of the pressure loss in the converging part of the duct is recovered in the diverging part of the

duct. The degree of pressure recovery is given by :



3. The continuity equation

The continuity equation is a statement of the conservation of mass. Consider the steady flow of a

fluid through a streamtube of varying cross sectional area as shown in figure 4. For steady flow the

mass of fluid entering the streamtube at section 1 must equal the mass of fluid leaving the

streamtube at section 2. The mass flow rate of fluid at any section along the streamtube must be

constant so that :

For an incompressible fluid the density is constant and the continuity equation can be written as :

For an incompressible fluid flowing in a converging duct it follows that as the area reduces then the

velocity must increase, whilst in a diverging duct as the area increases then the velocity must

decrease. Applying Bernoulli's equation if the velocity increases then the pressure must decrease

whilst as the velocity decreases the pressure must increase.

Figure 4: Element in a streamtube

Procedures:

1. Start the pump and initiate a flow of water through the test section. Regulate the flow to the

inlet head tank so that there is a small but steady overflow from inlet tank. Adjust the swivel

tube of the outlet tank to obtain a differential head of 50mm.



2. Measure the height of the water level in each manometer tube by marking the paper positioned

behind the tubes and record on the test sheet. Measure the time taken to fill the bench

measuring tank from zero to 10 liters and record.

3. Increase the differential head between the inlet and outlet head tanks by 5O mm increments,

until the water level in the centre manometer tubes drops off the scale. For each condition,

record the heights of liquid in the manometer tubes by once again marking the paper

positioned behind the tubes and measure the flow rate.

Results:

1. Record the results on a copy of the result sheet provided.

2. Calculate the flow rate for each set of results.

3. For each set of results calculate at the cross-section adjacent to each manometer tube and the

flow velocity.

4. Plot a graph of head against distance and also

against distance.

Quantity of water collected (liters)

Time to collect water (Sec)

Volumetric flow rate (m3/s)

Tapping number

1 2 3 4 5 6 7 8 9 10 11

Flow area

(mm2) 102.56 90.11 77.66 65.22 52.77 40.32 52.77 65.22 77.66 90.11 102.56

Static head

Velocity (m/s)

Total head

hydraulics lab

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