A fresh water on a reservoir is `10m` deep. A horizontal pipe `4.0 cm` in diameter passes through the reservoir `6.0 m` below the water surface as shown in figure . A plug secures the pipe opening.
.
(a) Find the friction force between the plug and pipe wall.
(b) The plug is removed. What volume of water flows out of the pipe in `1h`? Assume area of reservoir to be too large.

Answer

C, D

Explanation

(a) Force of friction
=pressure difference on the sides of the plug `xx` area of cross section of the plug
`=(rho gh)A`
`10^(3)(9.8)(6.0)(pi)(2xx10^(-2))^(2)`
`=73.9 N`.
(b) Assuming the area of the reservoir to be too large.
Velocity of efflux
`v=sqrt(2gh)= `constant
`:. v=sqrt(2xx9.8xx6)=10.84 m//s`
Volume of water coming out per sec,
`(dV)/(dt)=Av`
`=(pi)(2xx10^(-2))^(2)(10.84)`
`=1.36xx10^(-2) m^(3)//s`
`:.` The volume of water flowing through the pipe in 1 h.
`V=((dV)/(dt))t`
`=(1.36xx10^(-2))(3600)`
`=48.96 m^(3)`.