Worksheet: Venturi Meter – ME

Name(s):___________________________________________________________________________________________

Fill in all sections – These are today’s notes

Student Learning Objectives:

Students will be able to:1. Understand how velocity and pressure change as fluid passes through a venturi meter2. Understand the effect of diameter changes on velocity and pressure (may be nonlinear)3. Describe how energy transformation (one form to another) occurs along the axis of venturi meter4. Calculate flow rates from pressure difference (∆ P) data and compare to measured flow rates5. Calculate the venturi coefficient for the hands-on system used in class

DLM Schematic and Dimensions

Before Assembling your DLM

Draw the predicted velocity and pressure trends as water travels through the venturi meter through points 1 through 5 above. Explain your reasoning.

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D5 = D1 = 1.46 cmD3 = 0.524 cmD1 = 1.46 cm

Distance down venturi

Velocity

Flow

Velocity:

PressurePressure:

Velocity:Velocity:Velocity:Velocity:Velocity:Velocity:Velocity:Velocity:Velocity:Velocity:

Pressure:Pressure:Pressure:Pressure:Pressure:Pressure:Pressure:Pressure:Pressure:Pressure:

Worksheet: Venturi Meter – ME

Velocity and Pressure Trends in a Venturi Meter:1. Start the pump. Adjust the valve position, so that there is no water

leaking from the top of the manometer.2. Then mark and measure the water height in manometers 1 to 5. Plot

the pressure trend below. Remember that pressure is proportional to water column height.

3. Discuss the observed pressure trend. Why is the pressure at point 5 lower than the pressure at point 1?

4. The principle of mass conservation for steady, one-dimensional flow, with one inlet and one outlet can be represent as continuity equation:

ρi A i v i=ρ j A j v jwhere ρi = fluid density, Ai = cross sectional area and v i = average fluid velocity at section i.

Using the continuity equation above, complete velocity and area relationship statements with symbols (>, <, or =).a. Velocity at points 1 & 5:

Simplified continuity equation:

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Distance down venturi

Pressure

Worksheet: Venturi Meter – ME

Velocity relationship: v1v5 because A1 A5

b. Velocity at points 1 & 3:Simplified continuity equation:

Velocity relationship: v1v3 because A1 A3

5. Discuss how velocity varies with the diameter of the pipe at different sections in the venturi. Is it linear? Hint: use the continuity equation above.

6. The Bernoulli equation below gives the relationship between velocity head, pressure head and gravity head between two points. Match the terms in the Bernoulli equation with their definitions.

P1ρg

+Z1+v12

2 g=P2ρg

+Z2+v22

2g

Match these terms with their descriptions by arrows

Term in Bernoulli Equation Description

Piρg

Velocity head

Zi Pressure head

v i2

2gGravity head

7. Discuss how pressure varies with velocity, if Z1=Z2 (horizontal). Is it a linear? Hint: use the Bernoulli equation. Also explain how pressure varies with pipe diameter at different sections in the venturi? Hint: along with the Bernoulli equation, use the velocity and diameter relationship from continuity equation.

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Worksheet: Venturi Meter – ME

8. Based on the knowledge you gained from the continuity equation (also from the Bernoulli equation), draw a corrected velocity trend along the axis of the venturi.

9. For the valve settings in Table 1, run a series of experiments and measure the volumetric flow rate (with a beaker and cell phone stopwatch) and manometer water heights.

Table 1.

Valve settingV̇ measured= V/t

[mL/s]h1 [cm] h2 [cm] h3 [cm] h4 [cm] h5 [cm]

Fully Open

Partially Closed (1)

Partially Closed (2)

10. An energy transition occurs when one form of energy is converted to another. For example, when a ball begins rolling down a hill, potential energy is converted to kinetic energy as the ball accelerates and changes its vertical position.

What types of energy transitions occur in the venturi meter? How do kinetic energy, flow work, and frictional energy losses change between points 1 & 3 and points 1 & 5?

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5421 3

Distance down venturi

Velocity

Points 1 & 3

Worksheet: Venturi Meter – ME

Homework Problems Due:

1. What are the advantages and disadvantages of using a venturi meter compared to an orifice meter? (Hint: You will need to do some reading in your textbook and review on-line information.)

2. Derive the rearranged energy balance as shown below. Show your work. Hints: a) Start with the Bernoulli equation. Simplify it for points 1 and 3 (throat).b) Use the continuity equation to describe point 1 velocity in terms of throat velocity, v3.

c) Substitute V̇=v3 ∙π D3

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4.

d) Rearrange for V̇ and multiply your result by C v, the venturi coefficient.

V̇=(π D32/4 ) ∙C v

√1−( D3D1 )4 √ 2∆Pρ

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Points 1 & 5

Worksheet: Venturi Meter – ME

3. When deriving the equation above, what was ignored that makes C v necessary (do some reading on this; it is not just because you ignore frictional losses, though that is part of it). Why is the C v so close to 1.0?

4. Calculate the volumetric flow rate for each valve setting in Table 1 using both the data you collected the for outlet volume and time and the pressure drops between points 1 and 3. Compare the measured flow rates to those calculated from pressure drop measurements using the equation in Question 2. Use the literature value for the venturi coefficient (Cv) of 0.98.

Valve settingV̇ measured= V/t

[mL/s]∆P = gρ (h1 – h3)

[Pa]V̇ calculated[mL/s]

Fully Open

Partially Closed (1)

More Closed (2)

Discuss possible reasons for differences between V̇ measured and V̇ calculated .

5. Calculate the venturi coefficient from your data and compare it to the literature value of 0.98. Hint: Use the equation derived in question 2 above. You have flow rate and pressure drop data, and diameter values; how can you obtain C v? Consider using the slope from a linearized plot.

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Worksheet: Venturi Meter – ME

Cv =

Attach your plot to the end of this assignment.

6. From your data, how much energy per unit mass (multiply the head by gravitational acceleration constant) is being lost due to friction and dissipation of turbulent eddies between points 1 and 5? Compare that to how much energy would be lost in a straight pipe, of the same diameter as the venturi entrance at point 1, with a length equal to the distance between points 1 and 5 ( L1→3=9cm). Show your work below.

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