Mass Flow Rate Formula

The mass flow rate is the amount of liquid that moves across a unit area in unit time. It remains constant throughout a liquid due to the principle of conservation of mass. It varies directly with density, the velocity of the liquid, and the area of cross-section of pipe or tube through which the liquid is flowing. It is denoted by the symbol m. Its standard unit of measurement is kilograms per second (kg/s) and the dimensional formula is given by [M¹L⁰T^-1]. Its formula is equal to the product of the density of the liquid, velocity of liquid flow and the area of the cross-section of the pipe.

Formula

m = ρVA

where,

m is the mass flow rate,

ρ is the density of the liquid,

V is the velocity of the liquid,

A is the area of cross-section.

Sample Problems

Problem 1. Calculate the mass flow rate for a liquid of density 1.5 kg/m³ flowing with a velocity of 40 m/s through a pipe of cross-section 30 sq. m.

Solution:

We have,

ρ = 1.5

V = 40

A = 30

Using the formula we have,

m = ρVA

= 1.5 × 40 × 30

= 1800 kg/s

Problem 2. Calculate the mass flow rate for a liquid of density 3 kg/m³ flowing with a velocity of 50 m/s through a pipe of cross-section 40 sq. m.

Solution:

We have,

ρ = 3

V = 50

A = 40

Using the formula we have,

m = ρVA

= 3 × 50 × 40

= 6000 kg/s

Problem 3. Calculate the density of a liquid if its mass flow rate is 1500 kg/s flowing with a velocity of 30 m/s through a pipe of cross-section 50 sq. m.

Solution:

We have,

m = 1500

V = 30

A = 50

Using the formula we have,

m = ρVA

=> ρ = m/VA

=> ρ = 1500/(30 × 50)

=> ρ = 1500/1500

=> ρ = 1 kg/m³

Problem 4. Calculate the density of a liquid if its mass flow rate is 2400 kg/s flowing with a velocity of 20 m/s through a pipe of cross-section 60 sq. m.

Solution:

We have,

m = 2400

V = 20

A = 60

Using the formula we have,

m = ρVA

=> ρ = m/VA

=> ρ = 2400/(20 × 60)

=> ρ = 2400/1200

=> ρ = 2 kg/m³

Problem 5. Calculate the velocity of a liquid if its mass flow rate is 4500 kg/s with a density of 3 kg/m³ through a pipe of cross-section 30 sq. m.

Solution:

We have,

m = 4500

ρ = 3

A = 30

Using the formula we have,

m = ρVA

=> V = m/ρA

=> V = 4500/(3 × 30)

=> V = 4500/90

=> V = 50 m/s

Problem 6. Calculate the velocity of a liquid if its mass flow rate is 2400 kg/s with a density of 4 kg/m³ through a pipe of cross-section 60 sq. m.

Solution:

We have,

m = 2400

ρ = 4

A = 60

Using the formula we have,

m = ρVA

=> V = m/ρA

=> V = 2400/(4 × 60)

=> V = 2400/240

=> V = 10 m/s

Problem 7. Calculate the cross-section area of a tube through which a liquid flows with a mass flow rate is 3600 kg/s, density of 2 kg/m³ and velocity of 30 m/s.

Solution:

We have,

m = 3600

ρ = 2

A = 30

Using the formula we have,

m = ρVA

=> A = m/ρV

=> A = 3600/(2 × 30)

=> A = 3600/60

=> A = 60 m/s