As part of a processing of biofuels, water is pumped into a circular tank with a diameter Dt, as shown in Figure Q3. The flowrate into the tank is Q₁ and the flowrate out is Q₂. When the vessel is heated, water evaporates. The average velocity at which the vapour rises across the entire tank is vevap. You may assume that water has a density of pw, and vapour has a density of pv. Acceleration due to gravity is g. a) Find an expression for the rate of change of the mass of water in the tank. b) At time t = 0, the height of water in the tank is ho. Find an expression for the height as a function of time, h(t).

As part of a processing of biofuels, water is pumped into a circular tank with a diameter Dt, as shown in Figure Q3. The flowrate into the tank is Q₁ and the flowrate out is Q₂. When the vessel is heated, water evaporates. The average velocity at which the vapour rises across the entire tank is vevap. You may assume that water has a density of pw, and vapour has a density of pv. Acceleration due to gravity is g. a) Find an expression for the rate of change of the mass of water in the tank. b) At time t = 0, the height of water in the tank is ho. Find an expression for the height as a function of time, h(t).

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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Fluid Dynamics

The study of the flow of gases and liquids, usually in and around solid surfaces, is known as fluid dynamics in physics and engineering. Fluid dynamics, for example, can be used to evaluate the movement of air through an airplane wing or the surface of a vehicle. It can also be used in ship design to increase the speed at which ships pass through water.

Question

As part of a processing of biofuels, water is pumped into a circular tank with a diameter D₁,
as shown in Figure Q3. The flowrate into the tank is Q₁ and the flowrate out is Q2. When
the vessel is heated, water evaporates. The average velocity at which the vapour rises
across the entire tank is vevap-
You may assume that water has a density of Pw, and vapour has a density of pv.
Acceleration due to gravity is g.
a) Find an expression for the rate of change of the mass of water in the tank.
b) At time t = 0, the height of water in the tank is ho. Find an expression for the
height as a function of time, h(t).

c) An alarm is triggered when the pressure at the bottom of the tank exceeds Palarm.
Find an expression for the time at which the alarm goes off.
Q₁
evap
Q₂
D₁
Figure Q3: Water being pumped through a heated evaporation tank.

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