Question

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?

Answer 1

a. If dm/dt is kg/second, then

kg/second= ? * P= ?*nt/m^2
or ? has units of kg*m^2/Ns

but N is kg*m/s^2

or ?= kg*m^2/(kg*m/s^2 * s)
?= second/meter