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A pipe of diameter D is connected to a w...

A pipe of diameter `D` is connected to a water tank of large cross-sectional area in which water is maintained at a height `H` as shown in the figure. A nozzle of diameter `'d'` fitted at the end of the pipe discharges water into the atmosphere. Find the flow rate, given that the density of water is `p`. Also find pressure at point `C`. (`P_(0)` is the atmosoheric pressure)

Text Solution

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Taking the nozzle axis as the datum and applying Bernoulli's equation
`(P_(0))/(rhog)+H+0=(P_(0))/(rhog)+(v^(2))/(2g)+0`
`v=sqrt(2gH)`
Flow rate, `Q=(pi)/(4)d^(2)sqrt(2gH)`
Now, `(pi)/(4)d^(2)sqrt(2gH)=(pi)/(4)D^(2)v_(1)`
`v_(1)=(d^(2))/(D^(2))sqrt(2gH)`
Applying Bernoulli's equation at the water surface and at point `C`
`(P_(0))/(rhog)+H+0=(P_(c ))/(rhog)+H+h+(v_(1)^(2))/(2g)`
`P_(c )=P_(0)-(h+(Hd^(4))/(D^(4)))rhog`
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