Question

The tank initially contains 1000 m3 of crude oil. Oil is pumped into the tank through a pipe at a rate of 2 m3/min and out of the tank at a velocity of 1.5 m/s through another pipe having a diameter of 0.15 m. The crude oil has a constant specific volume of 0.0015 m3/kg. Determine (a) The mass of oil in the tank after 24 hours (in kg). (b) The volumetric of oil in the tank at that time (in m3).

Answer 1

(a) m = 1058346.67 kg

(b) V = 1587.52 m³

Step-by-step explanation:

`Inlet\ Volume\ Flow\ Rate = (2\ m^3/min)(1\ min/60\ s) = 0.0333\ m^3/s\\Outlet\ Volume\ Flow\ Rate = (Outlet\ Velocity)(Area) = (1.5\ m/s)(\pi)(0.15\ m/2)^2\\Outlet\ Volume\ Flow\ Rate = 0.0265\ m^3/s`

(b)

The volume of oil in the tank in 24 hours can be found as follows:

`Volume\ of\ Oil = m = Iinitial\ Volume + (Inlet\ Volume\ Flow - Outlet\ Volume\ Flow)(Time)\\V = 1000\ m^3 + (0.0333\ m^3/s - 0.0265\ m^3/s)(24*3600\ s)\\`

V = 1587.52 m³

(a)

Now, for the mass:

`Mass\ of\ Oil = m = (Volume)/(Specific Volume) = (1587.52\ m^3)/(0.0015\ m^3/kg)\\\\`

m = 1058346.67 kg