Fluid dynamics question?
Answer:
if i remember correctly, its been over a year, i think you will have to reduce the Reynold's Transport Theory or the Bernoulli equation based on certian assumptions such as fixed control volume, conservation of mass, constant density, etc. If i remember correctly one of the problems is that the discharge flow rate is not constant because of varying pressure. Check a text book, there should be some example problems and applicable assumptions.
Use the Bernoulli equation. It can be found in most unit operation books.
Shape of tank? Sphere or cylinder? Square?
http://hyperphysics.phy-astr.gsu.edu/hba...
This will help.
Bernoulli's Equation will work. Because it is hydrostatic pressure, the pressure can be put in terms of the hydrostatic force pushing down from the water and the area it acts on. The velocity of the water can then be found because you know Bernoulli's Equation is constant. Velocity can then be converted into volume flow rate by multiplying by the area of the hole giving you gallons per minute.
the equation i remember
d h[t] / dt = ( -b*Ao(2*g*h[t])^0.5 ) / A
thats square root of 2 * g * h[t]
I canceled out density
b is frictional coefficient of the hole
Ao = area of hole in tank
g = gravity
A= area of tank
h[t] = height of fluid level
You gotta solve the differential .
you'll get an
h[t] = equation
I guess then multiply the Area of the tank back to get V[t]
You're going to need to know the Area, the flowrate is going to be depending on the height of the water in the tank since more water = more force.
use continuity equation lor.
Q= velocity x cross-sectional area
at steady-state, A1u1=A2u2
again bernoulli's equation do play a part in this phenomenon as there are three types of energy involved(potential,kinetic and pressure energies)
i.e. P/(density)(g) + u2/2g +gz = constant
isnt it simple to use? :)
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