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
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