Mass Flow Rate Calculator
The mass flow rate is the mass of a substance that passes through a given surface per unit of time. It's a crucial concept in fluid dynamics, thermodynamics, and various engineering applications. Calculating it helps in understanding how much material is being processed, transported, or consumed.
Understanding Mass Flow Rate
The formula for mass flow rate ($\dot{m}$) is derived from the relationship between density, velocity, and the area through which the fluid is flowing:
$\dot{m} = \rho \times v \times A$
- Density ($\rho$): This is the mass per unit volume of the substance. Different substances have different densities. For example, water at standard conditions has a density of approximately 1000 kg/m³.
- Flow Velocity ($v$): This is the average speed at which the substance is moving across the cross-sectional area. It's usually measured in meters per second (m/s).
- Cross-sectional Area ($A$): This is the area of the surface perpendicular to the direction of flow. For a pipe, it's the area of the circular opening (πr²).
By multiplying these three values, you get the mass flow rate, typically expressed in kilograms per second (kg/s).
Example Calculation
Let's calculate the mass flow rate of water flowing through a pipe.
- Density of water ($\rho$) = 1000 kg/m³
- Flow Velocity ($v$) = 1.5 m/s
- Cross-sectional Area of the pipe ($A$) = 0.02 m²
Using the formula:
$\dot{m} = 1000 \text{ kg/m³} \times 1.5 \text{ m/s} \times 0.02 \text{ m²}$
$\dot{m} = 30 \text{ kg/s}$
Therefore, the mass flow rate of water in this scenario is 30 kilograms per second.