Question

The side wall of a wide vertical cylindrical vessel of height h = 75 cm has a narrow vertical slit running all the way down to the bottom of the vessel. The length of the slit is l = 50 cm and the width b = 1.0 mm. With the slit closed, the vessel is filled with water. Find the resultant force of reaction of the water flowing out of the vessel immediately after the slit is opened.

Answer 1

Consider an element of height dy at a distance y from the top. The velocity of the fluid coming out of the element is

v=√2gy 

The force of reaction dF due to this is dF=ρdAv², as in the previous problem, =ρ(bdy)2gy