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A steam of water flowing horizontally wi...

A steam of water flowing horizontally with a speed of `25m ^(s-1)` gushes out of a tube of cross-sectional area `10^(-3) m^(2)`, and hits at a vertical wall nearby. What is the force exerted on the wall by the impact of water

A

`1^@ C`

B

`0.1 ^@ C `

C

`10^@ C `

D

`0.01^@ C `

Text Solution

Verified by Experts

The correct Answer is:
A
Given area of cross - section `A= (5)/(sqrt(21) ) xx 10^(-3) m^2`
Time `= t= 10 s `
increase in temperature ` Delta theta=?`
Now as per question a cubic metre of water comes out of the nozzle of hose in 10 s
` therefore ( "change in volume ")/(" time taken ") = (dV )/(dt ) = (1 m^3)/(10 s)`
= cross sectional area ` (A) xx ` velocity of ejection (v )
`implies Av =(1)/(10) m^3 //s implies v =(1)/( 10 A) m//s `
Now when the water hits the rigid wall then its changes in kinetic energy will give rise its thermal energy
` therefore 1/2 ms^2 = ms Delta theta `
where `s=` specific heat capacity of water `= 4200 J kg^(-1) ""^(@) C^(-1)`
`implies Delta theta (v^2 )/(2s ) = ((1 )/( 10 A )) ^2 xx (1)/( 2s)`
`implies Delta theta = (1)/( 200 A ^2 S) = (1 xx 21)/( 200 xx 25 xx 10^(-6) xx 4200 ) implies 0 = 1^@ C `
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