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The mass flow rate of liquid material is defined as the mass of the liquid passing per unit of time. The SI units for speed are kilograms per second. The mass flow is directly proportional to the density, velocity, and cross-sectional area of the liquid. It's also known as the mass movement per unit of time.
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Mass Flow Rate Formula
The pace at which a huge fluid moves through a unit area is known as mass flow rate. The density, velocity, and size of the cross-section all influence mass flow. It is the movement of mass per unit of time, in other words. Its units are kilograms per second. The mass flow rate formula is as follows:
Mass Flow Rate
Mass Flow Rate = (density)*(velocity)*(area of the cross-section)
m = ρ v A
Where,
- ρ: Density of the fluid
- v: Velocity of the fluid
- A: Area or cross-section
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Concept of Mass Flow Rate
Because of the conservation of mass, the mass flow rate through a tube must remain constant. From the provided flow conditions, we can calculate the mass flow rate. The mass flow rate is the rate at which a huge fluid moves through a unit area. Obviously, the flow rate is determined by the fluid's density, velocity, and cross-sectional area. As a result, it is the mass movement per unit of time. It's measured in kilograms per second. As a result, the mass flow rate is defined as the mass of a liquid material moving through a unit of time.
Check Important Notes for Centripetal Acceleration
Points To Remember
- The mass flow is directly proportional to the density, velocity, and cross-sectional area of the liquid.
- The amount of mass traveling through an instrument over time is referred to as mass flow rate.
- If the mass flow remains constant as the temperature rises, the volume flow must rise to pass the same amount of mass (molecules) across the sensor.
- We can increase the mass flow rate indefinitely by simply increasing the velocity.
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Sample Questions
Ques 1. A fluid is moving through a tube at 10 m/s, the tube has a transverse area of 0.3 m2. The density of the fluid is ρ = 1.7 grams/m3. What is the amount of mass flowing through the tube? (1 mark)
Ans. The total mass of the fluid flowing is given by the formula, m = ρ v A.
m= 1.7 grams/m3 * 10 m/s 0.3 m2 = 5.1 grams/s
m= 5.1 grams/s
Ques 2. Given the density of a fluid as 1000 kg/m3, velocity as 50 m/s, and area of cross-section as 10 cm2, determine the movement of mass per unit of time. (2 marks)
Ans. Given,
- \(\rho\)= 1000 kg/m3
- V = 50 m/s
- A = 10 cm2 = 0.1 m2
m = \(\rho\)VA
m = 1000 x 50 x 0.1
m = 5000 kg/s
Ques 3. A fluid moves at 20 m/s through a tube. The tube has an area of 0.5 m2. The density of the fluid is 1.5 g/m3. Determine the movement of mass per unit of time. (2 marks)
Ans. Given,
- \(\rho\)= 1.5 g/m3
- V = 20 m/s
- A = 0.5 m2
m = \(\rho\)VA
m = 20 x 1.5 x 0.5
∴ m = 15 g/s
Ques 4. What is the difference between a mass flow rate and a volumetric flow rate? (2 marks)
Ans. The mass of a liquid traveling across a cross-sectional area per unit of time is known as mass flow rate. The volumetric flow rate is the amount of liquid that passes through in one unit of time.
Ques 5. The rate mass of fluid is 15 grams/s, is flowing in a tube at 0.7 m/s, and has a density of 1.5 grams/m3. What is the diameter of the tube? (3 marks)
Ans. 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 of a tube, also known as its cross-section, is equal to the area of a circle of radius R, as defined by A= R². We get the following expression by substituting in the formula for the area obtained from the m formula:
m / (ρ v) = π R²
Taking the square root on both sides of the following calculation and dividing it by
√ (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√ (15 grams/s / (1.5 grams/m3 * 0.7 m/s * 3.1416)) = D
D = 15.75 m.
Ques 6. Determine the mass flow rate of a given fluid whose density is 1300 kg/m3, velocity, and area of cross-section is 50 m/s and 40 cm2 respectively. (3 marks)
Ans. Given values are,
ρ = 1300 kg/m3
V = 50 m/s and
A = 40 cm2
= 0.40 m2
The mass flow rate formula is given by,
m = ρVA
m = 1300 × 50 × 0.40
m = 26000 kg/s
Ques 7. In Fluid Mechanics, what is the Mass Flow Rate? (2 marks)
Ans: The mass flow rate is the amount of liquid that moves per unit of time. To put it another way, the mass flow rate formula depicts the rate at which liquid passes through a unit area. The density and velocity of the liquid with the cross-sectional area are directly related to the fuel mass flow rate formula.
Ques 8. What's the Connection Between Mass and Volume Flow Rates? (2 marks)
Ans. The mass flow formula calculates how many molecules pass through a flowing gas. The space occupied by such molecules is measured by the volumetric flow. Because the gas is compressible, when the pressure or temperature of the gas varies, the volumetric flow rates can fluctuate dramatically.
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