A hose pipe used for gardening is ejecting water horizontally at the rate of `0.5 m//s`. Area of the bore of the pipe is `10 cm^2`. Calculate the force to be applied by the gardener to hold the pipe horizontally stationary.

Explanation

If ejecting water horizontally is considered as action force on the water, the water exerts a backward force (called recoil force) on the pipe as the reaction force.
`vecF=(dvecp)/(dt)=(d(mvecv))/(dt)=(dm)/(dt) vec v+m (dvecv)/(dt)`
As v, the velocity of ejected water is constant, `F= (dm)/(dt)vecv` , where `(dm)/(dt)` is the rate at Which mass of water is ejected by the pipe.
As the force is in the direction of velocity (horizontal), we can use scalars. `:. F= (dm)/(dt) v`
`(dm)/(dt)=(d(V rho))/(dt)=(d(Al rho))/(dt)=A rho (dl)/(dt)=A rho "v"`
where V = volume of water ejected
A = area of cross section of bore = `10 cm^2`
`rho = "density of water" = 1 g//cc`
`i` = length of the water ejected in time `t`
`dl/dt= v ="velocity of water ejected"`
`= 0.5 m//s = 50 cm//s`
`F= (dm)/(dt) v=(A rho v)v=A rho v^2=10 xx 1 xx 50^2`
=25000 dyne=0.25 N
Equal and opposite force must be applied by the gardener.