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A venturimeter is 37.5 cm. Diameter in m...

A venturimeter is `37.5 cm`. Diameter in mains and `15 cm`. Diameter in throat. The difference between the pressure of water in the mais and the throat is `23 cm` of Hg. Find the discharge in `litres//minunte`. Sp. Gravity of Hg. `13.56`.

Text Solution

Verified by Experts

The correct Answer is:
8400
Here h = 23 cm of Hg ` = 23 xx 13.56 cm` of water
` r_(1) = (37.5)/( 2) = 18.75 cm r_(2) = (15)/( 2) = 7 . 5 cm`
`a_(1) = pi r_(1)^(2) = pi (18 . 75)^(2) cm^(2) , r_(2) = pi r_(2)^(2) = pi ( 7 . 5 )^(2) cm^(2)`
Rate of flow
`Q = a_(1) a_(2) sqrt(( 2 gh)/( a_(1)^(2) - a_(2)^(2)))`
` = pi ( 18 . 75)^(2) xx pi ( 7. 5) ^(2) sqrt(( 2 xx 980 xx 23 xx 13 . 56)/([ pi ( 18 . 75 )^(2) ]^(2) - [ pi ( 7 . 5)^(2) ]^(2)))`
` pi xx (18 . 75 )^(2) xx ( 7 . 5)^(2) sqrt((2 xx 980 xx 23 xx 13.56)/((18.75)^(4) - (7.5)^(4))cm ^(3) s^(-1))`
`= pi xx (18 . 75 )^(2) xx ( 7 . 5) ^(2) sqrt(( 2 xx 980 xx 23 xx 13.56)/( 120432 . 13))`
` = 1.4 xx 10 ^(5) cm^(3) s^(-1)`
` = (1 . 4 xx 10 ^(5) xx 60)/( 1000) `= 8400 liter `"min"^(-1)`
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