Physics Assignment | Task Report | Doc

Task 1
a) Pressure in the pipe which is at an elevation of 100m from the city:
By applying Bernoulli’s equation. Taking point A as a source of water and Point B on city
(Pressure head + velocity head + datum head) at Point A = (Pressure head + velocity head +
datum head) at B
Since it is a pipe flow velocity head at point A and point B are same.
Pa + Za + velocity head at A = Pb + Zb + velocity head at B
Pa + Za = Pb + Zb (Since it is a pipe flow velocity head at point A and point B are same)
Pa + 100 = Pb + 0
Pa - Pb = 100m
The pressure is 100m in terms of the head. In terms of energy pressure = ρgh
= 1000 X 9.81 X 100 = 981 kPa
In open channel pressure in the city will be atmospheric because the velocity head will be
different at point A and B. The velocity in the city will be higher as compared to the point of
source. Higher velocity at the city will be compensated by pressure. So the pressures
difference at both the point A & B same.
b) Two main resistance of flow:
i) Loss due to viscosity(In laminar flow): Due to viscosity there exist velocity
gradient near the surface. At the surface velocity of the fluid is zero; it gradually
increases and reaches max limit. Due to this velocity gradient, there is a loss of
pressure head in the pipe which can be found by Hagen–Poiseuille
equation(Douglas et al. 2011)
Δp = 128μlQ_πd4
Loss due viscosity (In turbulent flow): frictional loss in turbulent flow is much
higher than laminar flow. Due to the separation of layers, eddy develops, and this
results in higher frictional losses.

ii) Loss due boundary layer: As boundary layer develops depth of flow decreases
due to decrease in depth velocity head increases and pressure head decreases. The
decrease in pressure is loss which occurs in pipe flow.
c) Effect of temperature on losses: As the temperature increases viscosity decreases. Due
to decreases in viscosity frictional loss and loss related to boundary layer decreases.
d) Difference between laminar and turbulent flow:
Laminar flow: when each layer of fluid flows following the smooth path and layers do
not interfere with each other is called laminar flow. When Reynolds number is less
than 2000 in pipe flow and less than 500 in open channel flow, then the flow is termed
as laminar flow.
Turbulent flow: When the layer of flowing fluid interferes with the subsequent layer,
and eddy develops due to high velocity, then flow pattern is termed as turbulent flow.
(Douglas et al. 2011)
e) Reynolds number: Ratio of inertia force and viscous force is called Reynolds number.
Mathematically it defined as Re = ⍴VD/μ
f) Reynolds number is used to identify the type of flow (laminar, transition or turbulent
flow).
For turbulent flow in pipe Re value should be greater than 2000. For open channel
flow Re must be greater than 500.
f) Boundary layer: boundary layer thickness is defined as that distance from the surface
where the local velocity equals 99 per cent of the free stream velocity. When the surface is
smooth, and Reynolds number is low boundary layer is not dependent upon roughness but
when Reynolds number is high, and the surface is rough boundary layer is dependent on
roughness. (Douglas et al. 2011)
g) Resistance to water flow can be reduced by decreasing viscosity. Viscosity can be reduced
by increasing temperature, reducing hardness of water by using lime soda, Ion exchange
method etc.
h) Parallel pipes can be laid to increase discharge without disrupting current supply.

Task 2
a) Data given:
Q = 30m3/s
B = 2
To find– Depth of flow at maximum discharge.
Sol.) Assuming rectangular channel.
Discharge per unit width (q) = 30/2 = 15
Critical depth of flow = 3
√ q2
g = 3
√ 152
9.81 = 2.841m
b) Data given:
Length of pipe = 2 KM
Discharge = 10m3/s
Friction factor = 0.006
Diameter of pipe = 1.5m
To find:
Head loss in pipe
Sol) Using Darcey Weisbach equation.
Hf = 8 f
π2
L
g
Q2
d5
= 8 X 0.006
π2
X 2000 X
g
102
1.55 = 13.05m
c) Data given:
Length of pipe = 2000Km
Discharge = 10m3/s
Friction factor = 0.006
Head available = 50m