Posted by **Anonymous** on Thursday, October 6, 2011 at 2:47am.

A 10 m high, 5 diameter cylindrical water tank has an inlet at the top and a drain at the bottom. The flow rate out of the tank depends on the pressure at the bottom of the tank via the following:

dm/dt = (10^-4)*(P_bot)

where P_bot is the absolute pressure in Pascal at the bottom of the tank. The tank is open to atmosphere at the top (P_atm) The density of water is 1000kg/m^3

(a) What are the units of 10

‐4

?

(b) What is the absolute pressure at the bottom of the tank in psia when the tank is 50% full?

(c) What is the gauge pressure at the bottom of the tank in psig when the tank is 50% full?

(d) At steady state, there is a specific inlet flow rate required to maintain a given water level in the tank.

Derive an equation that gives the inlet flow rate (in [kg/s]) required to maintain the water height (h) at

a given level, where h [m] is measured from the bottom of the tank upwards.

(e) Determine the inlet flow rate needed to keep the water level at 50% full.

(f) Assume that the tank is initially empty. At time t=0, the inlet is turned on at the flow rate you found

in part (e). How long does it take the tank to reach 30% full?

Think carefully…is the flowrate going out constant?

(g) How long does it take for the initially empty tank from part (f) to reach 50% full?

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