Explain any measurement errors and the discrepancy between measurement and theory.
HEAD LOSS IN PIPES
I. OBJECTIVES:
1. Understand the viscous effect on the friction head loss in pipes.
2. Compare the experimentally measured head loss to those predicted by empirical equations.
3. Compare friction losses in pipes of different sizes and flow rates.
4. Study the impact of major and minor head losses.
AI. THEORY:
For steady, incompressible flow the continuity equation reduces to:
(1)
Where Q is the volumetric flow rate and A is the cross-sectional area. 1 and 2 are any two arbitrary cross-sections. The energy equation on a per unit weight basis is:
(2)
Where V is the velocity, g is gravitational acceleration, z is the elevation, P is the static pressure, γ is the fluid specific gravity, and hL is the head loss. The head loss consists of two components major and minor losses. The major losses are associated with viscous effects in straight pipes while minor losses are from components in a pipe system. The major and minor head losses are calculated as follows:
(3)
(4)
Where KL is the loss coefficient.
The losses within the system depend on whether or not the flow in the pipes is laminar or turbulent. The dimensionless parameter Reynolds number is used to characterize the nature of the flow. For flow inside pipes:
· Re < 2000 — the flow is laminar
· 2000 < Re < 4000 — the flow is transitional
· Re > 4000 — the flow is turbulent
The friction coefficient (f) in equation 3 is a function of Re and relative pipe roughness (ε/D). For laminar flows it can be calculated using the relation:
(5)
For turbulent flows the friction coefficient can be found from Moody’s diagram or by using the following formula:
(6)
III. EXPERIMENTAL APPARATUS AND PROCEDURE
Experimental Apparatus:
· Head loss measurement test rig
· Smooth straight pipe
· Rough straight pipe
· 90° and 180° bends
· Ball valve
· Globe valve
· Backflow prevention valve
· Diameter change
· Differential pressure transducer
· Flowmeter
Figure 1: Head loss measurement test rig
IV. DATA ANALYSIS
Note: Before recording the pressures in the various elements in the pipe system all the air bubbles must be evacuated from the colored tubes on the back of the machine. To do this locate the purge valves on the back of the machine which are attached to the pressure transducer via a T-fitting. Attached at the perpendicular side of each T-fitting there are manually operated on-off valves. Open these valves by turning the lever so that it is parallel to the hose. Then go back to the computer and open each electronic valve individually allowing the air bubbles to escape. You may then close the purge valves.
Your experimental report must include:
1. The actual head loss in the pipes and components
2. The theoretical head loss
Note:
1. The roughness is ε= 0.7 mm
2. KL for the 90° bend is 0.69
3. KL for the backflow valve is 1.2
4. For the ball valve D1=1 in D2 = 0.85 in and D3=1 in
V. RESULTS AND DISCUSSION (MUST BE INCLUDED IN REPORT)
1. Compare the measured head loss with the theoretical predictions.
2. How does head loss change with flow rate?
3. Compare the smooth and rough pipe.
4. Compare the ball and globe valves.
5. Discuss any measurement errors and the discrepancy between measurement and theory.
6. Based on your experimental results, determine the pumping power required for a house with 25 feet of horizontal pipes (12.5 smooth and 12.5 feet rough), a height increase of 8 feet, ten 90° bends, five 180° bends, 2 ball valves, 2 globe valves, a backflow, and three area reductions. Are your results feasible?
BIBLIOGRAPHY
1. B.R. Munson, D.F. Young, T.H. Okiishi, Fundamentals of Fluid Mechanics, 5th Edition, John Wiley & Sons, 2006, ISBN 978-0-471-67582-2.
2. M.J. Moran, H.N. Shapiro, Fundamentals of Engineering Thermodynamics, 6th Edition, John Wiley & Sons, 22008, ISBN 978-0-471-78735-8.
3. T. G. Beckwith, R. D. Marangoni, J. H. Lienhard V, Mechanical Measurements, 6th Edition, Pearson Education, 2007, ISBN 0-201-84765-5.
4. J.P. Holman, Experimental Methods for Engineering, 7th Edition, McGrew-Hill, 2001, ISBN 0-07-366055-8.
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