Test: Power Transmission through Pipe - Civil Engineering (CE) MCQ

Efficiency of power transmission through pipe is given by,

Here, H = head available at inlet
h_f = frictional head loss
For maximum power transmission through pipe,

So, η_max = 66.67%

The power transmitted through a pipe is maximum when the loss of head due to friction is given by (H = head supplied),
h_f = H/3
Power transmission through pipes: 

• Power is transmitted through pipes by flowing water or other liquids through them. 
• Power transmitted through pipes will be dependent over the following factors as mentioned here. 

1. Rate of flow through the pipe.
2. Total head available at the end of the pipe

Now we will consider a tank with which a pipe AB is connected. Let us consider the following terms from figure

L = Length of the pipe, D = Diameter of the pipe, H = Total head available at the inlet of the pipe, V= Velocity of flow in the pipe, h_f = Loss of head due to friction, f = Co-efficient of friction 
Power transmitted at the outlet of the pipe can be determined by:
P = γQH_net
P = ρQgH_net

Concept:
The power extracted by the turbine,
P = η_h × ρ × Q × g × h      - (1)
Now, apply Bernoulli's equation for the turbine,


Where,
H = Available head, h = The head used for the power generation through  the turbine, Q = volume flow rate, ηh = the hydraulic efficiency of the turbine, h_residual = Residual head loss at the exit of the turbine, h_l,penstock = The head loss in the penstock
Calculation:
Given:
Q = 4000 l/s = 4 m³/s, h_l,penstock = 6 m, P = 900 kW, η_h = 90 %, H = 52 m
Using equation (1),
⇒ 900 × 103 = 0.90 × 1000 × 10 × 4 × h
⇒ h = 25 m 
Using equation (2),
⇒ 52 = 6 + 25 + hresidual
⇒ h_residual = 21 m

For Assertion:
If we are neglecting the entry and exit loss through the pipe and considering the friction loss only through the pipe, then net Power transmitted by the pipe,
⇒ P = ρ × Q × g × (H - h_f)

Head loss due to friction in pipe,

Where,
H = Net head available, v = Velocity through the pipe, L = Length of the pipe, D = Diameter of the pipe, Q = Volume flow rate, f= Darcy friction factor
For maximum power transmission through the pipe,
⇒ dP / dv = 0
By using equation (1),
⇒ h_f = H/3
⇒ The hydraulic power transmitted by a pipe through a certain distance by means of water under pressure will be maximum when the loss of head due to friction over this distance is one-third of the total head supplied.
For Reason:
A critical Reynolds number is determined as a limit where the laminar flow changes to turbulent flow. If the calculated Re is greater than the critical Reynolds number Re_c, the flow regime is turbulent; otherwise, the flow regime is laminar. The velocity corresponding to the critical Reynolds number is called the critical velocity. For laminar flow, the critical Reynolds number is 2300.
We calculate the Reynolds number by putting the velocity as average velocity in the formula,

L_c = Characteristic length, V_avg = The average velocity of the flow, μ = Dynamic viscosity of the fluid,, ρ = Density of the fluid,
⇒ The average velocity of flow should be equal to the critical velocity which corresponds to the laminar flow.

The efficiency of power transmission is given by

Here, H = head available at the inlet, hf = frictional head loss
For maximum efficiency
H_L = H/3
We get

η_max = 66.66%

The power transmitted through a pipe is maximum when the loss of head due to friction is given by (H = head supplied),
h_f = H/3
Power transmission through pipes: 

• Power is transmitted through pipes by flowing water or other liquids through them. 
• Power transmitted through pipes will be dependent over the following factors as mentioned here. 

1. Rate of flow through the pipe.
2. Total head available at the end of the pipe

Now we will consider a tank with which a pipe AB is connected. Let us consider the following terms from figure

L = Length of the pipe, D = Diameter of the pipe, H = Total head available at the inlet of the pipe, V= Velocity of flow in the pipe, h_f = Loss of head due to friction, f = Co-efficient of friction 
Power transmitted at the outlet of the pipe can be determined by:
P = γQH_net

Condition for maximum transmission of power: 
Now we will find here the condition for maximum transmission of power and it could be secured by differentiating the equation of power transmitted at the outlet of the pipe.

Concept:
Power is required to overcome losses, hf
Power = ρQgh
where h = frictional head loss
the frictional head loss will be equal to the pressure difference head
hence ρh = ΔP / ρg
Calculation:

Power = 9810 × 10^-3 × 10.19 = 100 W

Net available head (h) at the outlet of the pipe is given by:
h = H - hf
Where,
H is the total head at the inlet and hf be the head loss in the transmission.

Power available at the pipe outlet is given by:

For maximum power
dP/dV = 0 → H = 3h
∴ h_f = H/3.

Efficiency of power transmission is given by

For maximum efficiency
H_L = H/3
We get

η_max = 66.66%
Hence when the flow is such that one third of the static head is consumed in pipe friction, the power delivered by the given pipeline will be maximum.

The co-efficent of bend in a pipe depends on all the three parameters – radius of curvature of the bend, diameter (radius) of the pipe and angle of bend.