Surge tanks are often used to smooth flowrate fluctuations in liquid streams flo

Question

Surge tanks are often used to smooth flowrate fluctuations in liquid streams flowing between chemical processes. Consider a liquid surge tank with one inlet having a volumetric flowrate Fi, and one outlet having a volumetric flowrate F as shown in the following figure. Assume that the liquid density rho is a constant Find how the volume V of the tank varies as a function of time. If the tank has a constant cross-sectional area A and the outlet flowrate is proportional to the square root of the height of the liquid in the tank, find how the level or height of the liquid in tank varies as a function of time. It is given at steady state that A = 0.1m2, Fis = 0.01 m3/s, hs =0.5m , find the value and unit of alpha.

Explanation / Answer

i) dV/dt = Fi - F

Integrating, V = (Fi-F)*t

ii) dV/dt = A(dh/dt) = (Fi-F) = (Fi - h)

dh/(Fi - h) = dt/A

Integrating -2/^2 (Fi ln (Fi-h) - (Fi-h)) = t/A

iii) At steady state, dV/dt = 0.

So, F = Fi = 0.01 m^3/s

0.5 = 0.01

= 0.0141 (m^2.5)/s

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