A crude oil storage tank initially contains 1000 of crude oil. Oil is pumped into the tank through a pipe at a rate of 2 and out of the tank at a velocity of 1.5 m/s through another pipe having a diameter of 0.15m. The crude oil has a specific volume of 0.0015 . Determine:a) The mass of oil in the tank, in kg, after 24 hoursb) The volume of oil in the tank, in , at that time

This question is incomplete, the complete question is;

A crude oil storage 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 0.15m. The crude oil has a specific volume of 0.0015 m³/kg .

Determine : a) The mass of oil in the tank, in kg, after 24 hours b) The volume of oil in the tank, in m³, at that time ( after 24hrs )  

a) The mass of oil in the tank after 24hrs is 1059852.6667 kg  

b) The volume of oil in the tank, in m³, at that time is 1589.779 m³

Explanation:

Given that;

volume of tank v = 1000 m³

Discharge  (AV)₁ = 2 m³/min

specific volume (v) = 0.0015 m³/kg

a)

for one inlet, one exit control volume, we have]

d(mc)/dt = "m - "m

"m  = (AV)₁  / v

"m  = 2 / 0.0015

"m = 1333.33 kg/min = ( 1333.33 kg/min × 60 ) = 80,000 kg/hr

"m =  AV₂/v

AREA A = πr² = π(0.15m/2)²

so

"m =  ( π(0.15m/2)² × 1.5 m/s ) / 0.0015m³/kg

"m = 17.6714 kg/s = (17.6714 kg/s × 60 × 60 ) = 63,617.25 kg/hr

 d(m)/dt = 80000 - 63,617.25 =  16382.75 kg/hr

now after 24 hours, the mass of the crude oil tank is;

mc( 24 ) = ( 16382.75 × 24 ) + mass initially contained

so initial mass m = volume / specific volume

initial mass m = V / v = 1000 / 0.0015 = 666,666.6667 kg

Total mass = m + mc

Total mass = 666,666.6667 kg + (16382.75 × 24)  

Total mass = 1059852.6667 kg  

Therefore, The mass of oil in the tank after 24hrs is 1059852.6667 kg  

b)

Volume will be;

V = total mass × density

V = 1059852.6667 kg  × 0.0015 m³/kg

V = 1589.779 m³

Therefore, The volume of oil in the tank, in m³, at that time is 1589.779 m³