Fluid Mechanics
The water surface is at the position shown at t = 0 seconds. What is the rate of rise or fall velocity of the water at t = 19 seconds? What is it at t = 21 seconds?
Solution
From the conservation of mass
rho*Ai*V1 = rho*A*dh/dt + rho*Ae*V2
A*dh/dt = Ai*V1 - Ae*V2
D^2*dh/dt = Di^2*V1 - De^2*V2
144*dh/dt = 144*1 - 36*2
dh/dt = 0.5
dh = 0.5*dt
Integrating
h-h0 = 0.5*t
Where ho is the initial height
Delta(h) = 0.5*t
When t = 19 sec
Rise in water level is
Delta(h) at t = 19 sec = 0.5*19 = 9.5 ft
When t = 21 sec
delta(h) = 10.5 ft
Since the 10.5 >10 it will go to bigger tank then the rise is height is different
delta(h) = 10 + h1
let us calcualate h1
Let\'s find in this way
Assume that the entire tube is of at 12 in diameter and find the volume for this 0.5 ft extra
and now replace the same volume of water with bigger diameter of pipe
A*0.5 = A2*h1
12^2*0.5 = 24^2*h1
h1 = 0.125 ft
Delta(h) = 10.125 ft
.
Fluid Mechanics The water surface is at the position shown at t - 0 se.docx
1. Fluid Mechanics
The water surface is at the position shown at t = 0 seconds. What is the rate of rise or fall
velocity of the water at t = 19 seconds? What is it at t = 21 seconds?
Solution
From the conservation of mass
rho*Ai*V1 = rho*A*dh/dt + rho*Ae*V2
A*dh/dt = Ai*V1 - Ae*V2
D^2*dh/dt = Di^2*V1 - De^2*V2
144*dh/dt = 144*1 - 36*2
dh/dt = 0.5
dh = 0.5*dt
Integrating
h-h0 = 0.5*t
Where ho is the initial height
Delta(h) = 0.5*t
When t = 19 sec
Rise in water level is
Delta(h) at t = 19 sec = 0.5*19 = 9.5 ft
When t = 21 sec
2. delta(h) = 10.5 ft
Since the 10.5 >10 it will go to bigger tank then the rise is height is different
delta(h) = 10 + h1
let us calcualate h1
Let's find in this way
Assume that the entire tube is of at 12 in diameter and find the volume for this 0.5 ft extra
and now replace the same volume of water with bigger diameter of pipe
A*0.5 = A2*h1
12^2*0.5 = 24^2*h1
h1 = 0.125 ft
Delta(h) = 10.125 ft
