On the opposite sides of a wide vertical vessel filled with water two identical holes are opened each having the cross-sectional area `S=0.50cm^(2)` the height difference between them is equal to `Deltah=51cm` find the resultant force of reaction of the water flowing out of the vessel.

Explanation

Let the velocity of water, flowing through A be `v_A` and that through `B` ve `v_B`, then discharging rate through `A=Q_A=Sv_A` and similarly through `B=Sv_B`.
Now, force of reaction at A,
`F_A=rhoQ_Av_A=rhoSv_B^2`
Hence, the net force,
`F=rhoS(v_A^2-v_B^2)` as `vecF_AuarrdarrvecF_B` (1)
Applying Bernoulli's theorem to the liquid flowing out of A we get
`rho_0+rhogh=rho_0+1/2rhov_A^2`
and similarly at B
`rho_0+rhog(h+Deltah)=rho_0+1/2rhov_B^2`
Hence `(v_B^2-v_A^2)rho/2=Delta h rho g`
Thus `F=2rhogSDeltah=0*50N`