Mass Flow Rate Formula

The conservation of mass is a part of thermodynamics and it is a fundamental concept of physics. According to physics the mass of the substance should always remain constant. Hence, the mass is neither created nor destroyed, but it can modify from one form to another. The mass of any object can be determined by its volume, density, and area it occupies. 

The mass of a liquid substance passing per unit time is termed the mass flow rate. The mass flow rate can also be expressed as the rate of movement of liquid pass through a unit area. Here, the mass flow rate will vary as the density, velocity of the liquid varies. Also, the mass flow rate will increase as the cross-sectional area increases. So, the mass flow is directly proportional to the velocity of the liquid, density of the liquid, and area of the cross-section. The mass flow rate is the movement of mass per unit time. The mass flow rate can be expressed as m and the mass flow can be calculated in terms of  kg/s. 

Mass flow rate equation m = ρVA

Here, 

m denoted the mass flow rate

ρ denotes the density of the liquid.

V denotes the velocity of the liquid

A denotes the cross-sectional area. 

The cross-sectional area of a tube can be calculated as given below. 

Then, 

A = πr2

Here, r denotes the radius of the tube. 

By using the above mass flow rate of the water formula, we can also calculate velocity from mass flow rate. 

Problems Related to Mass Flow Rate 

Problem 1: Calculate the mass flow rate of a given fluid whose density is 700 kg/m3, velocity, and area of cross-section is 40 m/s and 30 cm2 respectively.

Solution:

As per given data

ρ = 700 kg/m3

V = 40 m/s and

A = 30 cm2

    = 0.30 m2

The formula for calculating mass flow rate (m)

m = ρVA

m = 700 × 40 × 0.30

m = 8400 kg/s

The mass flow rate m  for the above-given data is 8400 kg/s

Problem 2: Determine the density of the liquid? The mass flow rate of the liquid is 4800 kg/s. And the velocity and area of the cross-section are 30 m/s and 20 cm2 respectively.

Solution:

From the given values

m = 4800 kg/s

V = 30 m/s and

A = 20 cm2

= 0.20 m2

To calculate the density of the liquid from the above-given values. 

ρ = m/VA

ρ = 4800 / ( 30 * 0.20 )

ρ =  4800 / 6

ρ =  800 kg/m3

The density of the liquid ρ for the above-given data is 800 kg/m3