Unit: V-Flow Through Pipes. Flow Through Pipes Major Energy Losses - Darcy-Weisbach Formula -...

Unit: V-Flow Through Pipes

Flow Through Pipes

Major Energy Losses - Darcy-Weisbach Formula - Chezy’s Formula

Minor Energy Losses -Sudden expansion of Pipe - Sudden Contraction of Pipe - Loss at Entrance - Loss at the exit - Loss to an Obstruction - Loss Bend in Pipe - Loss in various Pipe fitting

Hydraulic GradientTotal energy linePipe in seriesPipe in ParallelFlow through branchesHydraulic Transmission of

pipe

Section I

Major Energy Losses

a) Darcy-Weisbach Formula:

Re ‹ 2000

Re 4000 to 106

b) Chezy’s Formula

Ex Find the head lost due to friction in a pipe of diameter 300 mm and length 50 m, through which is flowing at a velocity of 3 m/s.1) Darcy formula’2) Chezy’s formula for which C = 60Take V for water = 0.01 stoke.

Ans hf = 0.7828 m, hf = 1.665 m

Ex Find the diameter of pipe of length 2000 m when the rate of flow of water through the pipe is 200 lit/s and the head lost duet to friction is 4 m. Take the value of C = 50 in Chezy’s formulae.

Ans d = 0.553m

Ex An oil of Sp.gr. 0.7 is flowing through a pipe of diameter 300 mm at the rate of 500 lit/s. Find the head lost due to friction and power required to maintain the flow for a length of 1000m. Take v = 0.29 stokes.

V = Q/ARe = (V x d)/ v

Ans V = 0.073 m/s, Re =7.3 x 104, f =0.0048, hf = 163.18 m , P =560.28kW

Section II

Minor Energy Losses

1) Loss of head due to sudden enlargement

A1 V1 = A2 V2

2) Loss of head due to sudden Contraction

If Cc =0.62 , k = 0.375

If Cc is not given then the head loss

Ex Find the loss of head when a pipe of diameter 200 mm is suddenly enlarged to a diameter of 400 mm. The rate of flow of water through the pipe is 250 lit/s.

Ans he = 1.816 m, p2 = 12.96 N/cm2, P = 4.453 kW

Ex The rate of flow of water through a horizontal pipe is 0.25 m3/s. The diameter of the pipe which is 200 mm is suddenly enlarged to 400 mm. The pressure intensity in the smaller pipe is 11.772 N/cm2.Determine i) loss of head due sudden enlargementii) Pressure intensity in the large pipeiii) Power lost due to enlargement.

Ans he = 1.816 m, P2 = 12.96 N/cm2, P = 4.453 kW

3) Loss of head at the entrance of a pipe

4) Loss of head at the exit of a pipe

5) Loss of head due to an obstruction in pipe

6) Loss of head due to Bend in pipe

7) Loss of head in Various pipe Fittings

Ex Water is flowing through a horizontal pipe of diameter 200 mm at a velocity of 3 m/s. A circular solid plate of diameter 150 mm is placed in the pipe to obstruct the flow. Find the loss of head due to obstruction in the pipe if Cc = 0.62

Ans he = 3.311 m

Ex Determine the rate of flow of water through a pipe of diameter 20 cm and length 50 m when one end of the pipe is connected to a tank and other end of the pipe is open to the atmosphere. The pipe is horizontal and the height of water in the tank is 4 m above the centre of the pipe. Consider all minor losses and take f = 0.009 in the formula

Ans V = 2.734 m/s, Q = 0.08589 m3/s

Section III

Flow through pipe in series or Compound pipes

Ex The difference in water surface levels in two tanks, which are connected by tree pipes in series of length 300 m, 170 m and 210 m and of diameters 300 mm, 200 mm and 400 mm respectively, is 12 m. Determine the rate of flow of water if co-efficient of friction are 0.005, 0.0052 and 0.0048 respectively, consideri) Minor lossesii) Neglecting minor losses

Ans V = 1.407 m/s, Q = 0.09945 m3/s

A1 V1 = A2 V2= A3 V3

Flow through Equivalent Pipe

Ex Three pipes of lengths 800 m, 500 m and 400 m and of diameter 500 mm, 400 mm and 300 mm respectively are connected in series. These pipes are to be replaced by single pipe of length 1700 m. Find the diameter of the single pipe.

Ans d = 371.8 mm

Flow through Parallel Pipe

Q = Q1 + Q2

Ex A main pipe divides into two parallel pipes which again forms one pipe as shown. The length and diameter for the first parallel pipe are 2000m and 1 m respectively, while the length and diameter of 2nd parallel pipe are 2000 m and 0.8 m. Find the rate of flow in each parallel pipe, if total flow in the main is 3.0 m3/s. The co-efficient of friction for each parallel pipe is same and equal to 0.005

Flow through branched pipes

Ex Three reservoirs A, B and C are connected by a pipe system shown. Find the discharge into or from the reservoirs B and C if the rate of flow from reservoirs A is 60 lit/s. Find the height of water level in the reservoir C.Take f = 0.006 for all pipes.

Q1 +Q2 = Q3

Power Transmission through Pipes

Condition for maximum Transmission through Pipes

Maximum efficiency of Transmission of power

Ex A pipe of diameter 300 mm and length 3500 m is used for the transmission of power by water. The total head at the inlet of the pipe is 500 m. Find the maximum power available at the outlet of the pipe, if the value of f = 0.006.

Q = A x V

Prepared by, Dr Dhruvesh Patel

Prepared by, Dr Dhruvesh Patel