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Module 4
                                             Flow in pipes

   1- Losses in pipes

Pressure loss due to friction in a pipeline.
In a pipe with a real fluid flowing, at the wall there is a shearing stress retarding the flow, as shown
below.




The pressure at 1 (upstream) is higher than the pressure at 2.




We can do some analysis to express this loss in pressure in terms of the forces acting on the fluid.
Consider a cylindrical element of incompressible fluid flowing in the pipe, as shown
The pressure at the upstream end is p, and at the downstream end the pressure has fallen by p to (p-
 p).The driving force due to pressure (F = Pressure x Area) can then be written
                        driving force = Pressure force at 1 - pressure force at 2




Darcy formula for the loss of head in pipelines




An alternative form of Darcy formula if Q is the discharge
Example: page 104 information sheet

If Q = 2.73 m3/min , f = 0.01, L = 300 m , d = 150 mm


   2- Shock losses



                          P1                        P2
                          V1                        V2
                          A1                        A2



Head lost at enlargement hL


For continuity of flow
                           A1V1 = A2V2
                           V2 =
                           hL



Example 1 page 96
A pipe increases suddenly in diameter from 0.5 m to 1 m . a mercury U-tube has one leg
connected just upstream of the change and the other leg connected to the larger section a
short distance downstream. If there is difference of 35 mm in the mercury levels the rest of
the gauge being filled with water find the discharge.

Solution




Sudden contraction



                          P1                        P2
                          V1                        V2
                          A1                        A2
Example 2 page 101
A pipe carrying 0.06 m3 /s suddenly contracts from 200 mm to 150 mm diam. Assuming that
a vena contract is formed in the smaller pipe calculate the coefficient of contraction if the
pressure head at a point upstream of contraction is 0.655 m greater than at a point just down
stream of the vena contract.

Solution




Applications on pipelines problems




Examples 5, 6, 7, 8 and 9 page 106 - 113

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MET 212 Module 4

  • 1. Module 4 Flow in pipes 1- Losses in pipes Pressure loss due to friction in a pipeline. In a pipe with a real fluid flowing, at the wall there is a shearing stress retarding the flow, as shown below. The pressure at 1 (upstream) is higher than the pressure at 2. We can do some analysis to express this loss in pressure in terms of the forces acting on the fluid. Consider a cylindrical element of incompressible fluid flowing in the pipe, as shown
  • 2. The pressure at the upstream end is p, and at the downstream end the pressure has fallen by p to (p- p).The driving force due to pressure (F = Pressure x Area) can then be written driving force = Pressure force at 1 - pressure force at 2 Darcy formula for the loss of head in pipelines An alternative form of Darcy formula if Q is the discharge
  • 3. Example: page 104 information sheet If Q = 2.73 m3/min , f = 0.01, L = 300 m , d = 150 mm 2- Shock losses P1 P2 V1 V2 A1 A2 Head lost at enlargement hL For continuity of flow A1V1 = A2V2 V2 = hL Example 1 page 96 A pipe increases suddenly in diameter from 0.5 m to 1 m . a mercury U-tube has one leg connected just upstream of the change and the other leg connected to the larger section a short distance downstream. If there is difference of 35 mm in the mercury levels the rest of the gauge being filled with water find the discharge. Solution Sudden contraction P1 P2 V1 V2 A1 A2
  • 4. Example 2 page 101 A pipe carrying 0.06 m3 /s suddenly contracts from 200 mm to 150 mm diam. Assuming that a vena contract is formed in the smaller pipe calculate the coefficient of contraction if the pressure head at a point upstream of contraction is 0.655 m greater than at a point just down stream of the vena contract. Solution Applications on pipelines problems Examples 5, 6, 7, 8 and 9 page 106 - 113