# Mass Flow Rate to Volumetric Flow Rate: How and Problem Example

In the article we will discuss about the topic of Mass flow rate to volumetric flow rate and their related facts and the application of Mass flow rate to volumetric flow rate in the flied of engineering and their purposes.

For the getting value of volumetric flow rate from mass flow rate we need to divide the value of mass flow rate by the density.

## Mass flow Rate:

From the law of the conversion of mass we get a clear concept of the mass flow rate. The mass flow rate remains constant at a standard condition where time and pressure are fixed, if no mass added or removed from the external source to the object.

Mass flow rate can be defined as the mass of a liquid substance is moving at a fixed time period from a given a cross sectional area at a constant pressure and temperature.

With the help of the mass flow rate we could measure the molecules which are present in the flowing liquid through the measurement instruments.

## Volumetric flow rate:

In the piping system the volumetric flow rate is a vital factor. By this volumetric flow rate we could summarize the condition of the fluid.

In the inside of the pipe, the volume of fluid is flowing at a cross sectional area in a particular time period at the standard condition where the temperature and pressure is constant.

## Mass flow rate to volumetric flow rate formula:

In this article we will discuss about the topic of Mass flow rate to volumetric flow rate formula with detailed facts.

### Mass flow rate formula:

Mass flow rate = (Density of the fluid)* (Velocity of the liquid)* (Cross sectional area)

Mathematically it can be expressed as,

ṁ = ρVA

Where, ρ = Density of the flowing fluid

V = Velocity of the liquid substance

A = Cross sectional area

From the above equation the mass flow rate can be easily recognize that, the mass flow rate depend on the density, velocity and area and it is has direct relation with these three parameters

In another word mass flow rate also can be expressed as, ratio between the change in mass of the liquid substance to the change in fixed time.

Numerically it can be expressed as,

ṁ = dm/dt

The unit of the mass flow rate is kilogram per second (kg/s). In the equation the  is mainly used to classified from regular m, which we are generally used in work purpose.

### Volumetric flow rate:

The formula of the volumetric flow rate is,

Volumetric flow rate = (Flow velocity of the fluid) *(Cross sectional area)

Mathematically the form of the volumetric flow rate is,

Q = vA

Where, Q = Volumetric flow rate of the fluid

v = Velocity

A = Cross sectional area

In another word volumetric flow rate defined as the ratio between the changes of volume with the change in time.

It can be expressed as, Q = dV/dt

After study the formula of the volumetric flow rate we found that, the volumetric flow rate mainly dependent on the velocity of the fluid and area. The unit of this parameter is cubic meter per second. The dimension of the volumetric flow rate is, L3T-1.

## How do you convert mass flow rate to volume flow rate?

Mass flow rate of a piping system is the total mass is moving in a material.In numerically the mass flow rate expressed in pounds. In another way the volumetric flow rate is total volume is moving for a material. Numerically the volumetric flow rate expressed as cubic feet.

Convert mass flow rate to volume flow rate: At the beginning of the process the mass flow rate is divided by the density of the flowing fluid. After the division which result is coming that is the volumetric flow rate value. Numerically this is expressed as cubic feet.

In generally when we considering the measuring for flow that time liquid substance and gases are consider for an object. The mass of an object considered as density which contained the volume for the object. It can be express as pounds per cubic foot.

### Example:

Suppose the mass floe rate for an object is 200 pounds and density is 20 pounds in cubic feet, then the volumetric flow rate is,

Volumetric flow rate = Mass flow rate/Density = 200/20 = 10 cubic feet.

Using the mass flow rate and volumetric flow rate we get the relationship which is given below,

Q = ṁ/ρ

ṁ = Q x ρ

## Is volumetric flow rate the same as mass flow rate?

The volumetric flow rate mainly used to measure the amount of volume present in the fluid where as the mass flow rate used to measure the molecules in the flowing fluid.

Volumetric flow rate can be defined as the, in a 3 – dimensional area the present gas is flowing at a fixed temperature and pressure in a given time period.

Mass flow rate can be defined as the molecules present in the liquid substance are flow through in a given cross sectional area at standard condition.

## Problems on how to convert mass flow rate to volume flow rate:

### Problem: In the house of Rajesh he filled a water tank with the help of a pipe. The radius of the pipe is 3 cm. When Rajesh filled the tank he takes 2 hours. The velocity of the water which is flow through the pipe is 8.2 m/s. Assume the density of the water is 940 kg/cubic per meters. Find the volumetric and mass flow rate.

Solution: We know that,

Area for the pipe is,

The volumetric flow rate for the pipe is,

The mass rate for the pipe is,

## Problem: A water tank is totally full with a fluid. The fluid is flowing in the water tank at a speed of 90 meters per second. The total area of the water tank is 0.9 square meters. The fluid carry the density amount is 1.6 grams per cubic meters. Calculate the mass flow rate for the fluid in the water tank.

Solution: Given data,

ρ = 1.6 grams per cubic meters

A = 0.9 square meters

V = 90 meters per second

We know that,

ṁ =ρ VA

ṁ= 1.6 x 0.9 x 90 = 129.6 grams per second.

The mass flow rate for the liquid in the water tank is 129.6 grams per second.

## Problem: Determine the diameter of the pipe. A pipe which is attached with the water tank through this the water is flowing. The mass flow rate of the water which is flow by the pipe is 120 grams per second. The density and the velocity of the water respectively are 1.2 grams per cubic meter and 0.2 meter per second.

Solution: Given data are,

ṁ = 120 grams per second

ρ = 1.2 grams per second

V = 0.2 meter per second

We know that,

ṁ = ρVA

A = m/ρV = 120/1.2 x 0.2 = 500 sq. metre

Now we also know that, the formula of the cross sectional area is,

A = π x R2