Investigating Frictional Pressure Loss

Through Pipes and Fittings

First Semester

Lab Report 2017

L. J. Hughes

Student ID:

1789668

Partners and

date of experiment

Executive

Summary

Contents

1.

Introduction.. 2

2.

Theory. 2

3.

Method.. 4

4.

Results. 6

5.

Analysis and Discussion.. 6

6.

Conclusion.. 7

7.Bibliography. 7

1. Introduction

1.1. Measuring the pressure loss accurately

in pipes is important for maintaining efficiency in many plants and is

important …

1.2. Background info

1.3. This can be very usual in nuclear power

plants as knowing the exact flow rate in the pipe is important for cooling the PowerStation,

so it doesn’t overheat and for generating electricity as the water is turned

into steam. It is valuable to know the how both fluids will act and whether

they are turbulent and laminar is important as for cooling, you want turbulent

flow as it will be more efficient in cooling.

1.4. The aim of this experiment iss to

measure the pressure drops across a range of different pipe geometries and

compare these values with their theoretical ones. Also, experimental values we

will used to calibrate an orifice plate.

2. Theory

2.1. The Darcy-Weisbach equation is a way to

calculate the head loss due to the friction in the pipe as a function of the

velocity for an incompressible fluid. (Nevers, 1970)

2.2.

(2.2-2)

(2.2-3)

(2.2-1)

By taking a pipe of

uniform cross section, we can apply Bernoulli’s equation that the total energy

at section 1 is equal to the total energy in section 2.

The loss of energy is given by

(m), the pressure in the pipe is

(Pa), the velocity in the pipe is

(m/s), the density is

(Kg/m3), the acceleration due to

gravity is

(m/s2) and the elevation is given

as

(m).

Figure 1 – Fluid flow through a uniform

pipe of length H

As the

velocity is constant as the diameter is uniform throughout the pipe. As this is

a horizontal pipe the height from the datum line at sections 1 and 2 is the

same. Therefore, we can cancel

and

Then we can rearrange the equation to find it

in terms of a change in pressure.

is the frictional resistance (N) per unit wetted

area (m2) per velocity (m/s) is given by

,

multiplied by wetted area multiplied by the velocity squared.

is circumference of the pipe.

(2.2-4)

The force at section 1

is the pressure, at section 1, multiplied by the area, the force at section 2

is the pressure, at section 2, multiplied by the area. If one assumes that the

flow acts as a steady state flow, this means the sum of the forces in the

direction of flow are equal to zero. This is shown in the equation below.

(2.2-5)

If the areas are

factorised and equation (2.2-3) is substituted for

Then

equations (2.2-5) and (2.2-2) can be equated to give the following

(2.2-6)

equation.

(2.2-7)

The equation can be

further modified as

is equal to ?D and area is equal to ?D2/4

so the pi’s cancel and one of the D’s. Which simples to 4/D. f’/? can be

written as f/2, where f is the friction factor. Rearranging for

gives the Darcy-Weisbach equation.

(Munson, 2013)

MASS FLOW RATE PAGE 118

3.Method

3.1.

(3.1-1)

(3.1-2)

Two separate experiments

where done one measuring air and one measuring water. These fluids are very

different. 3.2-3.3 will cover air and 3.4-3.5 will cover water. It is important

before starting the experiment to calculate the flow rates for laminar and

turbulent regions. The flow rates for laminar and turbulent flow were

calculated using the following equation.

Rearranging

the equation for the velocity and using the equation of continuity which is:

(3.1-3)

One can arrive at the

result:

Since the flow rate is measured in litres

per minute by multiplying the result by

60000 will convert the number

from m3/s to L/min.

Therefore, the maximum flow rate for

the laminar region can be calculated.

The minimum flow rate for turbulent

flow can be calculated in the same way.

Figure 2 – Apparatus of pipes with air as the fluid

3.2. The manometer was connected to the first

stretch of pipe to measure the pressure drop across a 7mm internal diameter

pipe. (P1-P2) The balance was tared before the pump was turned on. The value of

the pressure drop was recorded for flow rates of 1,3,5 and 7. For the last pipe

(P9-P10) the values are 1,2,3,5 as some values went over the range of the

manometer.

The value of the manometer was given time to adjust to each flow rate. For

turbulent flow values of 21-24 were used. The experiment was repeated for all

the pipes. The air was able to escape from the pipe and the mass of the air escaping

was measured by a balance, to measure the mass flow rate.

3.3. In fitting (P7-P8) there was an orifice

plate, the values of the pressure drop calculated can be used to calibrate it.

These values can be used to plot a graph where flow rates and pressure drops

can be determined.

Figure 3 – Apparatus of pipes with water as the fluid

3.4. The globe value for the dark blue pipe

was obtained when both valves were closed. Then the light blue gate value was

opened at flow rates of 4,6,8,10 and 12. The pressure drops at each flow rate

was recorded for each of the pipes. Then the valve is closed, and the dark blue

gate valve is opened, and the pressure drops across the light blue pipe were

measured for the same values of flow rate.

3.5. For the impingement plate, the flow rate

was varied from 2 L/min to 34.4 L/min at random intervals to get a wide spread

of data, and the distance was recorded. This then can be used to calculate the

force on the plate and the force against distance can be graphed.

4.Results

5.Analysis and Discussion

5.1.

6.Conclusion

7.Bibliography

Munson, 2013. Fundamentals of Fluid Mechanics. 7th

edition ed. Singapore: John Wiley & Sons.

Nevers, N.

D., 1970. Fluid Mechanics. s.l.:Addison-Wesley Educational Publishers

Inc; First Edition edition (April 1970).

(Nevers, 1970)