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Minor head loss is head loss from valves or bends in a pipe. The K is a coefficient from experimental values in a predetermined table.

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Major head loss is head loss from a fully developed, incompressible pipe flow. This is mathematically defined by the Darcy-Weisbach equation. The f (friction factor coefficient can be calculated for laminar flow. In turbulent flow, the Reynold's number and relative roughness are relevant, and so Moody chart must be used.

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Assembly 1

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Head loss is is defined as the conversion of kinetic energy to thermal energy. Because there is an assumed constant diameter and velocity throughout the system, we use a simplified version of this formula we labelled Formula 1.

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Assembly 4

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Assembly 3

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Assembly 2

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Formula 1

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Reynolds number was determined using calculated velocity, pipe inner diameter & dynamic viscosity of water. The determined values of Reynold number shows that the flow is turbulent since the value is larger than 4000.

Using Haaland equation, the coefficient of friction can be determined given the calculated Reynold number and the pipe roughness is assumed zero since the pipe is new & clean.

The values of head losses; major & minor for all of the assemblies were determined using energy equation given the calculated pipe length, loss coefficient & the friction coefficient.

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The Reynolds number was found to be in the intermediate between turbulent and non turbulent depending on the velocity of the water. As such, the flow is assumed to be turbulent for all calculations.
The values for head lost coincided with our expectations as minor losses became the predominant factor in head loss once any flow disrupting sections were put in place, such as valves, flow meters, and bends. As previously discussed, any addition of restrictions or bends effectively dropped the pipe pressure and lowered average velocity. Major losses could have a larger influence in linger lengths but since the assembly contained very little piping the major losses found were very small.
It is apparent that valves offer the greatest head loss if not fully opened. Semi-closed valves not only reduced pressure head but they also reduced flow effectively lowering the impact of major losses on the system. The findings coincide with the energy equation for non compressible fluids which states that change in pressure will be related to the change in height and to the head losses (Major and Minor) caused by friction in the pipe as well as losses due to non linear pipe components.

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The laboratory consisted of multiple separate experiments to allow us to determine head losses due to various systems. We initially determined the expected Reynolds number by using the velocity of fluid flowing through the system as well as the roughness of the PVC piping to find a point on the moody diagram.
Using this information along with velocity of the fluid (from the calibrated flowmeters) it was possible to determine any values for major and minor losses in the system as well as the total head loss and the friction coefficient.
As is expected, assembly 1, consisting mainly of linear sections of pipe with relatively few bends had the largest part of its loss in Major Losses (1.97cm out of a total 2.76cm).

Assembly 2, with the three inline valves was influenced greatly by minor losses. The minor losses increased drastically as the valves were closed. Since closing the valves affected the stream velocity, major losses were also reduced drastically although total head loss increased.

Assembly 3, consisting of two identical legs, each containing two valves were nearly identical and offered head losses so similar that the differences could be related to various uncertainties in the measurements.

Assembly 4,  consisting of one leg with two valves and another leg with five 45 degree elbows displayed the concept that the bends offered more losses than the valves even though the pipe diameter remained the same throughout the bends.

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In a constant diameter piping system in which the pipe flow is fully developed, the head loss may be calculated. This calculation is based off of the sum of major and minor losses.
Minor Losses: Pipe components such as elbows, valves etc.
Major Losses: Friction loss in straight sections of pipe.

The losses for each system may be calculated by observing the pressure change (Δp) in the system. To complete the energy equation, many values must be taken into account: the pressures at inlet and outlet, elevation changes, fluid density, average velocity, friction factor and pipe length and diameter. These values can be incorporated into the formula below (formula 1) to help us determine an unknown in the formula. Most importantly, the pressure differential is used to find head losses.

Theoretical aspects of each lab so far has been used towards the completion and understanding of this lab.   The knowledge on how to calculate a flowrate using a hall sensor flowmeter was invaluable to the completion of this lab. The second most useful lab was lab 2, in which manometers were explored. These devices now allowed us to measure differences in pressure by measuring the height of a water column.

The main calculations determining head loss will be based on the K values given in Munson et al. (for minor head loss) and on our calculations for the calculated Reynolds number for a straight section of pipe (for major head loss).

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Initial set up:
1. Calibrate the flow meter by using a stop watch and time how long the water takes to fill up a 2L container.
2. Compare this to previous experimental data.
3. Calibrate both flow meters

Apparatus 1: Simple
1. Measure and record pressure differential
2. Collect data from flow meter

Apparatus 2: Ball valves
1. Open the gates fully
2. Measure and record pressure differential
3. Collect data from flow meter
4. Repeat steps 2 and 3 while opening all the gates 1/3, and then repeat again for the gates at 2/3

Apparatus 3: Symmetric 2-leg assembly
1. Measure and record pressure differential
2. Collect data from flow meter of the first leg
3. Collect data from flow meter of the second leg
***IMPORTANT NOTE: DO NOT PLACE THE  FLOW METER WITHIN 6” OF AN OPENING AT EITHER END***

Apparatus 4: Asymmetric 2-leg assembly
1. Measure and record pressure differential
2. Collect data from flow meter of the first leg
3. Collect data from flow meter of the second leg

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The purpose of this experiment is to examine experimental pressure differentials and flow rates in an assortment of pipe apparatuses in order to determine the friction factor  for 1/2” clear PVC pipe in laminar and turbulent flow, as well as investigate the effect pipe construction designs have on energy loss.