Question

A closed hemispherical shell of radius R is filled with fluid at uniform pressure p. The net force
of the fluid on the curved portion of the shell is given by:
A. 2πR2p
B. πR2p
C. 4πR2p
D. (4/3)πR2p
E. (4/3)πR3p

Answer 1

Answer:

pi*r^2*P

Explanation:

It is because the area of the circle is pi*r^2, the pressure is acting on total area, so we have to multiply it with P.

Answer 2

A closed hemispherical shell of radius R is filled with fluid at uniform pressure p.

We have to find the net force of the fluid on the curved portion of the shell.

see the diagram as shown in attached figure,

It is being shown that the pressure acting on the curved surface area (pressures exerted on each and every elementary surface area) is equal to the pressure acting on the flat surface area.

hence, the pressure on the curved portion of the shell = pressure acting on the flat surface of the shell = P

but area of flat surface of the shell = πR²

we know, pressure = force/area

∴ force on the curved portion of the shell = P × πR² = πR²P

Therefore the net force of the fluid on the curved portion of the shell is given by πR²P