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The reading of pressure meter attached w...

The reading of pressure meter attached with a closed pipe is `3.5 xx 10^(5)Nm^(-2)`. On opening the value of the pipe, the reading of the pressure meter is reduced to `3.0 xx 10^(5) Nm^(-2)`. Calculate the speed of the water flowing in the pipe.

Text Solution

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As the pipe is closed initially, fluid velocity `v_(1) = 0`. Pressure `P_(1) = 3.5 xx 10^(5) N m^(-2)`
When the value is opened,
Let the speed of water = `v_(2)`
Pressure `P_(2) = 3.0 xx 10^(5) N m^(-2)`
Applying Bernoulli's equation to horizontal flow
`P_(1) + (1)/(2) rho v_(1)^(2) = P_(2) + (1)/(2) rho v_(2)^(2)`
`P_(1) = P_(2) + (1)/(2) rho v_(2)^(2)`
`rArr v_(2) = sqrt((2)/(rho)(P_(1)-P_(2))`
`= sqrt((2 xx 0.5 xx 10^(5))/(10^(3)))" "["Density of water" = 10^(3) kg m^(-3)]`
`v_(2) = 10 m s^(-1)`
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