# Mass Flow Rate Formula

Mass Flow Rate is the rate of movement of a massive fluid through a unit area. Mass flow depends on the density, velocity of the fluid and the area of the cross section. Meaning, it is the movement of mass per unit time. It's units are kg/s. The formula for mass flow rate is given:

Mass Flow Rate = (density)*(velocity)*(area of the cross section)

m = ρ v A

Where we have:

ρ: Density of the fluid

v: Velocity of the fluid

A: Area or cross section

Mass flow rate Formula Questions:

1) A fluid is moving through a tube at 10 m/s, the tube has a transverse area of 0.3 m^{2}. The density of the fluid is ρ = 1.5 grams/m^{3}. What is the amount of mass flowing through the tube?

Answer: The total mass of the fluid flowing is given by the formula, m = ρ v A.

m= 1.5 grams/m^{3} * 10 m/s 0.3 m^{2} = 4.5 grams/s

m= 4.5 grams/s

2) The rate mass of a fluid is 9 grams/s, is flowing in a tube at 0.5 m/s and it has a density of 1.5 grams/m^{3}. What is the diameter of the tube?

Answer:The total mass of the fluid flowing is given by the formula, m = ρ v A. From this equation, we can obtain a formula for the area of the tube by dividing for ρ and v.

m / (ρ v) = A

The area or cross section of a tube is the area of a circle of radius R,given by A= π R^{2}. Substituting in the formula obtained for the area from the m formula, we obtain the following expression,

m / (ρ v) = π R^{2}

Dividing the above formula by π and taking the square root on both sides

√ (m / (ρ v π)) = R, and the diameter is two times the radius.

2√ (m / (ρ v π)) = 2R = D

Using the values the formula gives, 2√ (9 grams/s / (1.5 grams/m^{3} * 0.5 m/s * 3.1416)) = D

D = 3.9 m.

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