Question

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.

Answer 1

Before opening the pipe,
`P_(1) = 3.5 xx 10^(5) Nm^(-2), upsilon_(1) =0`
After opening the pipe
`P_(2) = 3 xx 10^(5) Nm^(-2) , upsilon_(2) = ? ,rho= 10^(3) kg m^(-3)`
Since the height of water does not change therefore the potential energy of the liquid will be same before and after opening the value .
Hence, `P_(1) + 1/2 rho upsilon_(1)^(2) = P_(2)+1/2 rho upsilon_(2)^(2)`
or `3.5 xx 10^(5) + 1/2 xx 10^(3) (0)^(2)`
`= 3 xx 10^(5) +1/2 xx 10^(3) xx upsilon_(2)^(2)`
or `1/2 xx 10^(3) xx upsilon_(2)^(2) = (3.5 - 3) xx 10^(5) = 0.5 xx 10^(5)`
or `upsilon_(2)^(2) = (2 xx 0.5 xx 10^(5))/(10^3) = 100 or upsilon_(2) = 10 ms^(-1)`.