Transcript Unit: V-Flow Through Pipes Flow Through Pipes Major Energy Losses - Darcy-Weisbach Formula - Chezy’s Formula Hydraulic Gradient Total energy line Pipe in series Pipe in Parallel Flow through.

Unit: V-Flow Through Pipes
Flow Through Pipes
Major Energy Losses
- Darcy-Weisbach Formula
- Chezy’s Formula
Hydraulic Gradient
Total energy line
Pipe in series
Pipe in Parallel
Flow through branches
Hydraulic Transmission of
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
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 = 60
Take 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/A
Re = (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 enlargement
ii) Pressure intensity in the large pipe
iii) 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, consider
i) Minor losses
ii) Neglecting minor losses
A1 V1 = A2 V2= A3 V3
Ans V = 1.407 m/s, Q = 0.09945 m3/s
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 coefficient 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=AxV
Prepared by,
Dr Dhruvesh Patel