Question

A pump discharges a liquid into a tank at the rate of 0.032 m³/s. The tank, 1.5 m in diameter and 4.20 m in height can hold 3500 kg of liquid. The density of the liquid and mass flow rate of the liquid handled by the pump are respectively,
1. 471.57 kg/m³ and 16 kg/s
2. 471.57 kg/m³ and 15 kg/s
3. 481.57 kg/m³ and 16 kg/s
4. 481.57 kg/m³ and 15 kg/s
5.

Answer 1

Correct Answer - Option 2 : 471.57 kg/m³ and 15 kg/s

Concept:

Let us assume that the tank is cylindrical.

Volume of tank = \(\frac{\pi}{4}d^2h\)

Density of liquid = \(\frac{Mass}{Volume}\)

Mass flow rate = Density × Volume flow rate

Calculation:

Given:

Q = 0.032 m3/s, d = 1.5 m, h = 4.20 m

Volume of tank = \(\frac{\pi}{4}d^2h\)

Volume of tank = \(\frac{\pi}{4}× 1.5^2× 4.2=7.418\;m^3\)

Density of liquid = \(\frac{Mass}{Volume}\)

Density of liquid = \(\frac{3500}{7.418}=471.80\;kg/m^3\)

Mass flow rate = Density × Volume flow rate

Mass flow rate = 7.418 kg/m³ × 0.032 m3/s

Mass flow rate = 15.097 kg/sec