REYNOLDS NUMBER ENERGY LOSSES DUE TO FRICTION (Topic 4)
REYNOLDS NUMBER ENERGY LOSSES DUE TO FRICTION (Topic 4)
REYNOLDS NUMBER ENERGY LOSSES DUE TO FRICTION (Topic 4)
TOPIC 4
REYNOLDS NUMBER AND
ENERGY LOSSES DUE TO
FRICTION
CC303 - HYDRAULIC 1
( PLO1;CLO1;LD1;C3 )
LEARNING OUTCOMES
Upon completion of this course, students should be
able to:
Explain clearly the basic principles and
characteristics of fluid mechanics, and fluid flows in
pipe and open channel (C3)
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( PLO1;CLO1;LD1;C3 )
4.1 Understand the behaviour of fluids
flowing in pipes
4.1.1
4.1.2
4.1.3
4.1.4
Type of Flow
i- Laminar flow.
Diagram
4.1
V1
V1=V2
V- Non-Uniform flow
Nota:V V1
V1
V1
V1
Q1 =
A1V1 =
Q2
A2V2
Vd
Re
=vd
Reynolds number
Experimental Reynolds
- The experiment is designed to see how the flowing in
a pipe, ie whether it is laminar, turbulent or
intermediate.
- This experiment was
initiated by the :
Prof. Osborne Reynold
- Prof. Osborne conclude that
flow condition be affected by
dynamic viscosity, density, diameter & velocity
Example 1
Fluid flow in a pipe diameter of 30 cm with a
velocity of 0.21m/s and the kinematic
viscosity 1.14mm2/s, calculate the Reynolds
number and specify the type of flow
Re
vd
0.21x0.30
1.14 x10 6
= 55263
Example 2
Diameter of 300 mm and a length of a pipe
which passes by with a discharge 0.053
m3/s, density of oil is 950 kg/m3 and
kinematic viscosity is 2.1 x 10 m2/s.
Determine the Reynolds number and type of
flow.
Given :
2
d = 300 mm
Q = 0.053 m3/ s
= 2.1 x 10 m2/s
A = 0.3 = 0.071 m2
3
Get the velocity of flowing first :V = Q/A = 0.053/ 0.071 = 0.75 m/s
Re = vd = 0.75(0.3)
2.1x10 4
( PLO1;CLO1;LD1;C3 )
4.2.1
4.2.2
4.2.3
4.2.4
4.2.5
4.2.6
Contents
Darcy-Weisbach formula
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HEAD LOSS
2 TYPES OF HEAD LOSS
MAIN LOSSES
- Darcy-Weisbach
formula
- Hf= 4fLV2
2gd
= fLQ2
3d5
MINOR LOSSES
- Entrance loss
- Exit loss
- Suddenly
enlargement
- Suddenly
Contraction
- Bend
- Valve
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FORMULA
MAIN LOSSES:
- Energy losses due to friction in pipe system
- Darcy-Weisbach formula
Hf= 4fLV2
2gd
@
= fLQ2
3d5
f = friction coefficient
l = pipe length (m)
v = velocity (m/s)
d = pipe diameter (m)
Q = flowrate (m3/s)
EXAMPLE 1
Calculate the head loss (energy) due to friction in the
pipe 500 m long and 20 cm diameter when water flow
with a velocity of 3m/s. Take f (coefficient of friction) =
0.01.
Given:
=
=
=
=
500 m
20 cm
3 m/s
0.01
Used formula
hf =
hf = 4 ( 0.01) ( 500) ( 3 )2
2 x 9.81 (0.2)
= 45.87 m
EXAMPLE 2
Calculate the head loss (energy) as the
resistance to friction in the pipe 300 m long
and 150 mm diameter when the flow rate is
2.75m3/min. (f = 0.01 )
Length of pipe
Diameter
=
Flowrate
=
=
300 m
150 mm
2.75 m3/ min
EXAMPLE 3
Calculate the head loss (energy) as the resistance to friction in
the pipe 300 m long and 150 mm diameter when the flow rate
is 2.75m3/min. (f = 0.01 )
Length of pipe
Diameter
Flowrate
=
=
=
300 m
150 mm
2.75 m3/ min
4. f .l.v 2
Used formula hf =
2 gd
From formula flowrate Q = AV
V = Q/A
= 0.046
( 0.15)2/4
= 2.6 m/s.
hf =
4 (0.01)(300 )(2.6 )2
2(9.81)(0.15)
27.56 m
Q = 2.75 m3/min
Change into m3/s
Q = 2.75 m3/60 s
= 0.046 m3/s
EXAMPLE 4
Head difference between the two end pipes
of 300mm diameter, 250m long and is 1.5m.
calculate the flow rate through the pipe if
the coefficient of friction is 0.01.
Given: a head difference (hf) = 1.5 m
The pipe length = 250 m
Diameter = 0.3 m
Solution :
f .l.Q
hf = 3d
1.5 = 0.01( 250 ) Q2
3 ( 0.3 )5
Q = 0.0661 m3/s
2
EXAMPLE 5
A tank was built four miles of a student
dormitory that can accommodate 5000
students. Water delivered from the tank to
the hostel with a pipe. Every student in a
dormitory with 200 liters per day. Water is
pumped to the hostel for 20 hours a day. If
the head losses due to friction is 20m of
water and the pipe friction coefficient is
0.008, calculate the diameter of the pipe
used.
Given: a head difference (hf) = 20 m
The pipe length = 200 m
The coefficient of friction = 0.008
hf
fl Q2
3d5
20 = 0.008(4000)(0.01389)
3 (d )5
d =
Kadaralir Q = 5000x200
= 1 x 106 liter
= 1x106 x103
20 jamx60 x60
= 0.01389m3/s
Where,
L -- length
Dynamic viscosity
of pipe
v - velocity
acc. of gravity
d - diameter
EXAMPLE 1
Water with a dynamic viscosity 1.49x10-3 Ns/m2 flows
through a pipe of 0.3 cm in diameter with a velocity of
0.9m/s. The length of the pipe is 9m. Given f =16/Re
a) Calculate the Reynolds number and state the type of
flow
b) Calculate the head loss due to friction, using HagenPoisulle formula
c) Calculate the head loss due to friction, using DarcyWeisbach formula
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