Solution Found!
Applying Conservation of MassData are provided for the
Chapter 4, Problem 4P(choose chapter or problem)
Data are provided for the crude oil storage tank shown in Fig. P4.4. The tank initially contains \(1000 \mathrm{~m}^3\) of crude oil. Oil is pumped into the tank through a pipe at a rate of \(2 \mathrm{~m}^3 / \mathrm{min}\) and out of the tank at a velocity of \(1.5 \mathrm{~m} / \mathrm{s}\) through another pipe having a diameter of \(0.15 \mathrm{~m}\). The crude oil has a specific volume of \(0.0015 \mathrm{~m}^3 / \mathrm{kg}\). Determine
(a) the mass of oil in the tank, in kg, after 24 hours, and
(b) the volume of oil in the tank, in \(\mathrm{m}^3\), at that time.
Questions & Answers
QUESTION:
Data are provided for the crude oil storage tank shown in Fig. P4.4. The tank initially contains \(1000 \mathrm{~m}^3\) of crude oil. Oil is pumped into the tank through a pipe at a rate of \(2 \mathrm{~m}^3 / \mathrm{min}\) and out of the tank at a velocity of \(1.5 \mathrm{~m} / \mathrm{s}\) through another pipe having a diameter of \(0.15 \mathrm{~m}\). The crude oil has a specific volume of \(0.0015 \mathrm{~m}^3 / \mathrm{kg}\). Determine
(a) the mass of oil in the tank, in kg, after 24 hours, and
(b) the volume of oil in the tank, in \(\mathrm{m}^3\), at that time.
ANSWER:
Part (a)
Step 1 of 6:
A tank contains a particular volume of crude oil initially. The inlet tube pumps oil at a volumetric rate and the outlet tube releases the oil at a speed. We are going to find the mass of oil in the tank after 24 hours.
The volume flow rate of the inlet (AV)1 = 2 m3/min = 0.0333 m3/s
The initial volume of oil V1 = 1000 m3
The speed at the outlet v2 = 1.5 m/s
The diameter of the outlet D2 = 0.15 m (radius r = 0.075 m )
The specific volume of oil v = 0.0015 m3/kg
The initial time t1 = 0
The final time t2 = 24 h = 86,400 s