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# MINOR LOSSES IN PIPE FLOW

الكلية كلية الهندسة     القسم  الهندسة البيئية     المرحلة 3
أستاذ المادة عدي عدنان جهاد الخيكاني       05/10/2012 16:33:54
Additional frictional losses occur at pipe entry, valves and fittings, sudden decrease or increase in flow area or where direction of flow changes.
The frictional losses other than pipe friction are called minor losses. In a pipe system design, it is necessary to take into account all such losses.
These losses are generally expressed as hf = C u_m^2/2g where C is constant, the value of which will depend on the situation and is called the loss coefficient. The expression is applicable both for laminar and turbulent flows.
(i) Loss of head at entrance: At the entrance from the reservoir into the pipe, losses take place due to the turbulence created downstream of the entrance. Three types of entrances are known.
(a) Bell mouthed: This is a smooth entrance and turbulence is suppressed to a great extent and C = 0.04 for this situation.
(b) Square edged entrance: Though it is desirable to provide a bell mouthed entrance it will not be always practicable. Square edged entrance is used more popularly. The loss coefficient, C = 0.5 in this case.
(c) Reentrant inlet: The pipe may sometimes protrude from the wall into the liquid. Such an arrangement is called reentrant inlet. The loss coefficient in this case is about 0.8.
(ii) Loss of head at submerged discharge: When a pipe with submerged outlet discharges into a liquid which is still (not moving) whole of the dynamic head u2/2g will be lost. The loss coefficient is 1.0. The discharge from reaction turbines into the tail race water is an example. The loss is reduced by providing a diverging pipe to reduce the exit velocity.
(iii) Sudden contraction: When the pipe section is suddenly reduced, loss coefficient depends on the diameter ratio. The value is 0.33 for D2/D1 = 0.5. The values are generally available in a tabular statement connecting D2/D1 and loss coefficient. Gradual contraction will reduce the loss. For gradual contraction it varies with the angle of the transition section from 0.05 to 0.08 for angles of 10° to 60°.
(iv) Sudden expansion: Here the sudden expansion creates pockets of eddying turbulence leading to losses. The loss of head hf is given by

Loss of head = (u1 – u2)2 / 2g.

where u1 and u2 are the velocities in the smaller and larger sections. Gradual expansion will reduce the losses.

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