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(solution) so the first part is finding the current rate of inflow into


so the first part is finding the current rate of inflow into reservoir. I used the mass balance dV/dt = Qin- Qout, and dV/dt is surface Area * rate of rise As a result, i got 2220 m^3/hr, my TA said i did it correctly for the first part, but then the problem is the second part i was trying to calc by finding the volume from 0 cm to 20 cm and the volume from 20 cm to 40 cm separatley and add them together and divide it by time (3 days ) and Qin for 3days -this value , then that give us minimum rate of water that dam operator should let pass for 3 days to keep level below 40 cm , but my TA it won't work. can you help me on doing the second part?  


Homework #1

 

MAE 122

 

Fall Quarter, 2016 Due: 10/6/2016 11:59am (Midnight!)

 

via TritonEd 1. A lake has a 2 m warm surface layer (20 degC) above a deep cold layer (15 degC). Wind along

 

the surface induces a velocity that is approximately uniform in the warm layer of T

 

2

 

U surf air CDU wind

 

water

 

H

 

where CD = 0.001 is a drag coefficient, Usurf is the velocity of the surfacewater layer, Uwind is the

 

wind speed and air, water are the air and water densities, H is the layer thickness, and T is the

 

time that the wind has been blowing. The flow in the surface layer leads to shear at the

 

between the warm and cold layers. If the wind speed is 10 m/s ,

 

interface that drives mixing

 

how long will it be before we can expect any mixing to span the full layer depth?

 

2. Write down the Navier-Stokes equations for a viscous, incompressible fluid, and briefly

 

describe each of the terms. What is meant by a steady flow?

 

Consider a steady flow with velocity scale U and length scale L. What non-dimensional

 

parameter describes the effects of viscous forces?

 

Non-dimensionalize the equations for steady flow using these scales and show how this

 

parameter enters the equations. Estimate the value of this dimensionless parameter for:

 

(i)

 

flow past a Formula 1 race car

 

(ii)

 

flow of wind around the trunk of a palm tree

 

(iii)

 

flow around a blue fin tuna

 

(iv)

 

flow around a golf ball 3. Shortly after a torrential rain, the water level in a reservoir behind a dam rises at the rate of 1 cm

 

per hour while the water allowed to pass beyond the dam remains set at 1500 m3/hour. Knowing

 

that the reservoir surface area is 7.2(104) m2, determine the current rate of inflow into the

 

reservoir (in m3 per hour). When the water level increases past 20 cm of its initial height, it

 

overflows into a flood channel that increases the area by 30%. If this rate of inflow is expected

 

to persist for three days but the reservoir level may not be allowed to rise by more than a total of

 

40 cm, does more water needs to be released at the dam than at the current rate? What is the

 

minimum rate of water that the dam operator should let pass for those three days to keep the

 

level below 40 cm?

 


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