Test: Flow Through Pipes - 1 - Civil Engineering (CE) MCQ

For instantaneous closure of valve, the pressure head at valve end is,
Δh = CV₀/g
Time period for travel of pressure wave from one end to the other is,
t = L/C
Therefore velocity of pressure wave,
C = L/t
and  Δh = LV₀/gt

Re_c = 2000 For critical flow
Viscosity, v = 0.01 Stokes 
VD/v = 2000
Velocity of flow,
V = (2000 x 0.01)/1 = 20cm/s
Flow at critical Reynolds number,
Q = V x πD²/4 = 20 x π/4 x 1
= 15.7 cm³/s = 0.0157 I/s

We know that critical time is given by,
T₀ = 2L/C ⇒ T₀ = (2 x 2000)/1000 = 4s.
Actual time for valve closure, T = 4s.
We know that if T < T₀, then the closure is known as rapid closure or instantaneous closure. Therefore the peak water hammer pressure will be equal to the water hammer pressure head for instantaneous closure of the valve at the downstream end i.e. 60 m.

If H is the total supply head and h_f is the loss of head due to friction, then head available at the outlet of pipe (neglecting the minor losses) is H - h_f. If Q is the discharge through the pipe , V is the velocity of flow and L and D are the length and the diameter of the pipe respectively, then from Darcy-Weisbach equation we have,

and 
The power available at the outlet of pipeline is given by,

⇒ 
For a given pipe and head at the entrance, the condition for the maximum power transmitted through the pipe line may be obtained by differentiating Pw.r.t V and equating it to zero.
∴ 

⇒ h_f = H/3

dp/dx = dτ/dy is valid for a steady uniform laminar flow.

P/ρg is pressure head or static head.
V²/2g is velocity head or dynamic head or kinetic head.
P/ρg + V²/2g is stagnation head.