Investigating cooling. 1.4. The aim of this experiment

Investigating Frictional Pressure Loss
Through Pipes and Fittings

First Semester
Lab Report 2017

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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)