A cylindrical vessel of inner radius m with a flat horizontal bottom holds water and…
PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Kinematics, conservation laws and ideal flow · Kinematics, conservation laws and ideal flow
Fluids and Continuum Physics, Ch Euler's equation and Bernoulli's theorem
Problem
A cylindrical vessel of inner radius 0.15 m with a flat horizontal bottom holds water and is spun steadily about its vertical axis at 2.0 revolutions per second. The water turns with the vessel as a rigid body, and the free surface is open to the atmosphere. In this state the water on the axis stands 0.16 m deep above the bottom. Water density 1000 kg m−3, g=9.8 m s−2.
((a)) Find the height of the free surface at the wall above its lowest point on the axis.
((b)) Find the gauge pressure on the bottom of the vessel at the axis, and at the wall. (In rigid-body rotation the acceleration of each parcel is horizontal, so the vertical variation of pressure is the hydrostatic one of Chapter 1.)
((c)) The vessel is now brought to rest and the water settles to a uniform depth of 0.25 m. A small hole of area 0.50 cm2 is opened in the bottom at the centre. Treating the flow from the surface to the hole as steady, inviscid and incompressible along a streamline, and noting that the vessel's cross-section is very large compared with the hole so that the surface speed is negligible, find the speed of the water leaving the hole.
((d)) Find the volume flow rate out of the hole.