Puneet Singh KalsiINTRODUCTION

THEORY/METHODOLOGY

RESULTS

A working pipeline was built around the criteria that were given that would connect the two tanks provided. The pipeline would be constructed using various lengths of pipes, several types of valves (e.g. isolating valve, non-return valve etc.), a centrifugal pump and various pipe fittings such as connectors and a rotameter. Varying the flowrate using the rotameter, pressure values were taken for the minimum, half maximum and maximum flowrate and the results were recorded and the experiment was repeated another 2 times to get more precision in results and to spot the trend more easily. These would fulfill the aims and objectives of our experiment which are as follows: q  To be able to work with a colleague to design and construct a functioning pipeline which

satisfies the guidelines given in the First Year Practical Workbook 2015-2016 q  To record the pressure at the maximum, half maximum and minimum flowrate q  To determine the relationship and correlation between the flowrate and pressure by using the

Bernoulli’s equation and Friction head equation.

All state variables within this experiment were constant and the only varying quantities are the flowrate and the pressure. Therefore the whole system is at a steady state which allows for the application of Bernoulli's equation assuming the flow is frictionless and incompressible (Smith, n.d.). Where P is pressure, ρ is the density of water, g is acceleration due to gravity, u is the velocity and h is the height. The Continuity equation can also be applied to this experiment.

The results show that pressure is inversely proportional to the volumetric flowrate as when flowrate increases, the pressure decreases. The graph backs this up as it has a negative gradient giving the plot a negative correlation. Theoretically, this is correct and is justified by the calculations made using the Bernoulli’s equation and Friction head. Bernoulli’s equation shows that the head loss calculated is directly proportional to the pressure. An increase in flowrate leads to a decrease in pressure and by the principle of proportionality, so does the head loss ΔH (as seen by the calculation). For the friction head equation, friction factor needs to be calculated (with the use of a moody diagram). By principle, as the flowrate increases, so does the friction factor, i.e., they are directly proportional. The equation proves that friction loss is directly proportional to the friction factor which means that flowrate is directly proportional to the head loss (Hf). This makes sense as the grater the flow rate is, the greater the volume of water per unit time is moving along the surface of the copper tubes leading to greater loss of energy though friction. Another part of the moody diagram that was needed to calculate the friction factor was the Reynolds number. Reynolds number determines the type of flow of water. It can be either laminar, transitional or turbulent (unpredictable), being laminar if its under 2300, transient if its between 2300-4000 and turbulent if its above 4000 (Engineering Toolbox, n.d.). The calculations revealed that the flow of water in our experiment was turbulent at half maximum and maximum. The above conclusively show that the objectives of the experiment were met.

The experiment was set out to determine the relationship between the volumetric flow rate and pressure. A pipeline was constructed

in order to do this by mounting 2 tanks on a metal frame and connecting the tanks via the use of various lengths of copper

tubes. Varying the flow rate of water through the pipeline allowed us to take pressure readings which helped us determine that

as the volumetric flow rate increases, the pressure decreases.

Fig. 1 Process Flow Diagram of the pipeline constructed

REFERENCES1. Smith, J.M., Van Nes, H.C. and Abott, M.M. (n.d.). Introduction to Chemical Engineering Thermodynamics. 7th ed. New York City: Mcraw-Hill. p208-210. Last accessed 26/11/2015 2 . Lecture Notes from Transport Phenomena and information from demostrator in the labs. Last accessed 26/11/2015 3. Engineering Toolbox. (n.d.). Darcy-Weisback Equation for Pressure and Head Loss. Available: http://www.engineeringtoolbox.com/darcy-weisbach-equation-d_646.html. Last accessed 26/11/2015. 4. Engineering Toolbox. (n.d.). Laminar, Transitional and Turbulent Flows. Available: http://www.engineeringtoolbox.com/laminar-transitional-turbulent-flow-d_577.html. Last accessed 27/11/2015.

Fig. 2 Image of the pipeline constructed

P/ρg + u2/2g + h = constant (1)

Q = uA (2) Where Q is the volumetric flow rate and A is the cross sectional area of the pipe. The Bernoulli’s principle states the principle of the conservation of energy in fluids (Lecture notes). Therefore, the equation can be extended and the extended version can be used to incorporate the calculation of the loss of energy by friction and losses through the small gaps in the connectors (also known as head loss) during fluid flow in the pipe. Where ΔH is the head loss, P1 u1 h1 are the initial conditions and P2 u2 h2 are the final conditions. An alternative way is to calculate the friction head which can be used to calculate the loss of energy by friction only (Engineering toolbox, n.d.). The equation also contains a dimensionless friction factor known as the Fanning friction factor (which is a ¼ of the Darcy friction factor) and can be calculated using the moody diagram and the Reynolds number. The Friction head equation is: Where Hf is the friction head, f is the friction factor, L is the length of the pipe and D is the diameter of the pipe. Assumptions o  There are no leakages through any connectors, valves, pumps or pipes as leakages would result to not all water

being transferred to tank B and also in release of pressure which would reduce the accuracy of the pressure measurements.

P1/ρg + u12/2g + h1 = P2/ρg + u2

2/2g + h2 + ΔH (3)

Hf = f x 4L/D x u2/2g (4)

Table 1: Pressure measurements taken during the experiment

Table 2: Observed results converted to SI units

Table 3: Derived Results

Fig. 3 Pressure Vs Flowrate graph

o  The flowrate of the water through the pipeline remains consistent as fluctuations in flowrate would cause fluctuation in pressure readings taken which would tamper with the data collected.

Volumetric Flow Rate , (L min-1) (±0.25)

Pressure, (lb in-2) (±0.5) RUN 1 RUN 2 RUN 3 AVERAGE

Minimum (0) 23.20 23.10 23.10 23.13 Half Maximum (4) 14.50 13.50 13.50 13.83 Maximum (8) 5.00 4.80 4.50 4.77

Volumetric Flow Rate, (m3 s-1) (±8.33 x 10-6)

Pressure, (Pa) (±1.72 x 103) RUN 1 RUN 2 RUN 3 AVERAGE

Minimum (0) 159958.4 159268.9 159268.9 159498.7 Half Maximum (6.67 x 10-5) 99974.0 93079.2 93079.2 95377.5 Maximum (1.33 x 10-4) 34473.8 33094.8 31026.4 32865.0

Velocity, u (m s-1)

Reynolds Number, Re

Friction Factor, f

Friction Head, Hf (m)

Head Loss, ΔH (m)

0 0 0 0 15.2 0.38 6544.2 0.036 0.165 8.70 0.76 13088.4 0.027 0.494 2.33

y = -9E+08x + 159231 R² = 0.99995

0

20000

40000

60000

80000

100000

120000

140000

160000

180000

-0.00002 0 0.00002 0.00004 0.00006 0.00008 0.0001 0.00012 0.00014 0.00016

Pres

sure

(Pa)

Volumetric Flowrate (m3 s-1)

Pressure Vs Flowrate

Y-Value 1

Linear (Y-Value 1)

There is room for improvement in the experiment, for example the nuts could be tightened a lot using a spanner to reduce leakage which is the main source of error in this experiment. Another improvement could be to use a digital device to measure the flow rate to get more precise readings than the rotameter to reduce parallax error. All the equipment should also be calibrated regularly to decrease the possibility of a systematic and/or zero setting error. Nomenclature

Symbol Meaning Units

P, P1, P2 Pressure

ρ Density of water

g Acceleration due to gravity

u, u1, u2 Velocity

h, h1, h2 Height

Q Volumetric Flowrate

A Cross-sectional area

ΔH Head loss

Hf Friction head

f Friction factor

L Length of the pipe from pump to tank B

D Diameter of the copper tubes

Table 4: Nomenclature

Tank A

Tank B

Pressure Guage

Isolating Valve

Rotameter

Control Valve

Non-return Valve

Centrifugal pump Drain