On the opposite sides of a wide vertical vessel filled with water, two identical holes are opened, each having cross section area a. The height difference between them is equal to `h`. Find the resultant force of reaction of water flowing out of vessel.

Explanation

Volume of water/sec from opening `A = av_1`
Reaction force on `A`
`F_A` = rate of change of momentum
=`(rho av_1) v_1 = rho av_1^2`
=`rho a. 2gh_1`
Reaction force on `B`
`F_B = rho av_2^2`
=`rho a. 2gh_2`
Net reaction force
`F = F_B - F_A = 2 rho ag(h_2 - h_1)`
=`2 rho a g h`.
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