Torricelli\'s Law of Fluid Flow the conical small, round hole at the bottom of t
ID: 2874744 • Letter: T
Question
Torricelli's Law of Fluid Flow the conical small, round hole at the bottom of the tank which drains through a Consider 1. Torricelli's law states that when the surface of the water is at height h, the water drains with a velocity it would have if it fell freely from height h, Find the terminal velocity of an object that falls from height h(0) ho using the standard gravity differential equation. d2h. V 294 us 2. The rate at which the water is flowing out of the tank is the area of the hole times the velocity of of the draining water. Write the differential equation for the change in volume of the water in the tank. V d6 3. The volume of the tank at time t is given by the cross-sectional area times the height, V(t) Tr2h(t). Differentiate this with respect to time to find another differential equation for the change in volume of the water in the tank.Explanation / Answer
Let the volume of the tank 'Q'
Area of the hole be 'A' , velocity of draining water be 'v'
as the water is leaving the tank, rate of change of volume of tank = -dQ/dt (-ve sign because the volume decreases)
Given that the rate of change of volume = Area of hole times the velocity of drain
==> -dQ/dt = A * v
==> dQ/dt = -Av
v can be found out by the law of conservation of energy principle
let the mass of water flowing out be 'm'
==> kinetic energy of water flowing out = potential energy of water of mass m at height h
==> (1/2)mv2 = mgh
==> v = (2gh)
==> dQ/dt = -A(2gh)
==> Differential equation is dQ/dt = -A(2gh)