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Hydraulic System POWER TRANSMISSION THROUGH PIPE

POWER TRANSMISSION THROUGH PIPE

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We were discussing the basics of shear stress in turbulent flow, minor head losses in pipe flow, hydraulic gradient and total energy line, basic concept and working of syphon, flow through pipes in series, flow through pipes in parallel and flow through branched pipes in the subject of fluid mechanics, in our recent posts. 

Now we will go ahead to see the concept of power transmission through pipes, efficiency of power transmission and we will also find here the condition for maximum transmission of power, in the subject of fluid mechanics, with the help of this post. 

Power transmission through pipes 

Power is transmitted through pipes by flowing water or other liquids flowing through them. Power transmitted through pipes will be dependent over the following factors as mentioned here. 
  • Weight of the liquid flowing through the pipe 
  • 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 pipe 
hf = Loss of head due to friction 
f = Co-efficient of friction 

Power transmitted at the outlet of the pipe will be determined with the help of following formula as mentioned here. 

Efficiency of power transmission 

Efficiency of power transmission will be determined with the help of following formula as mentioned here. 

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.

Above expression is the condition of maximum transmission of power. We can conclude from above equation that power transmitted through a pipe will be maximum when the head loss due to friction will be one-third of the total head at inlet. 

Maximum efficiency of transmission of power 

As we have already secured the equation of efficiency of power transmission through pipe and it is as mentioned here. 

η = (H- hf)/H 

Now we will use the value of hf in above equation to secure the maximum efficiency of transmission of power and we have following result as mentioned here. 

η = (H- hf)/H
η = (H- H/3)/H

η = 66.7 %

Further we will go ahead to find out the concept of flow through nozzles, in the subject of fluid mechanics, with the help of our next post.  

Do you have any suggestions? Please write in comment box. 

Reference: 

Fluid mechanics, By R. K. Bansal 
Image courtesy: Google 

Also read  

Streamline and equipotential line 
Dimensional homogeneity 
Buckingham pi theorem 
Difference between model and prototype 
Lagrangian and Eulerian method 
Types of fluid flow 
Discharge or flow rate 
Continuity equation in three dimensions 
Continuity equation in cylindrical polar coordinates
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