# Mass Flow Rate And Power: Effect, Relation , Problem Examples

The mass flow rate and power is calculated by knowing value of each other.

The relation of mass flow rate with these power, Heat power = m° * q, work power = m° * w

The heat power is the input heat to the system. The work power is the work output from the system. Both powers are varying directly with the mass flowing through the system.

The mass flow rate is expressed as below,

Mass flow rate (m°) = Density (ρ) * Cross sectional area (A) * Velocity (v)

Where,

Density (ρ) in kg/m3

Cross-sectional area (A) in m2

Velocity (v) in m/s

The other unit of power is horse power. The horse power unit is used widely in pump , eletcric motor, turbine etc.

The terms power is used more in electronic equipment as compared to energy.

## How to calculate mass flow with power?

The mass flow rate can be calculated with many expressions.

The power is expressed concerning the mass flow rate, P = m° w. The power is directly varying with respect to the mass flow rate.

The power equation written in terms of the mass flow rate,

P = m° w

Where,

P = Power in W (watt)

m° = Mass flow rate in Kg/s or LPM

w = Specific work in J/kg (Joule/kg). (Where J = N m)

The power discussed here is fluid power. The fluid power varies directly with the variation in the mass flow rate. The mass flow rate is the rate of fluid passing through a particular point or location.

It is measured in the kilogram per second or litre per minute (second).

Example

Suppose the mass flow rate of the system is 10 kg/s and the specific work is 50 J/kg. Find the power required?

• m° = 10 kg/s
• w = 50 J/kg
• Power (P) =?

Power = m° w

Power = 10 * 50

Power = 500 watt

Power = 0.5 kW

## Mass flow rate and power relation

The power can be obtained from the value of mass flow rate.

The power is equated in relation to the mass flow rate, P = m° w. The power is product of the mass flow rate and specific work.

the power can be expressed with volume flow rate as below,

Power = V° p

Here,

V° = Volume flow rate in m3/s,

p = pressure in N/m2

The unit of power is m3/s *N/m2. It is generally given as N m/s or Juale/s.

The unit of mass flow rate is kg/s (kg of Mass passed into second). It is denoted by m°.

We can convert the volume flow rate into the mass flow rate if we know the density of the fluid circulating through the system.

The mass flow rate can be obtained from the volume flow rate by multiplying it with fluid density.

m° = V° * ρ

Where,

ρ = density of the fluid in kg/ m3

The theorem of the Torricelli given statement  for the transformation of the potential energy (PE) into the kinetic energy (KE) as below:

The velocity of the fluid = Square root of (2 * g * h)

Where,

g = Gravitational acceleration in m/s2

h = head in m

V = Velocity of the fluid in m/s

## Mass flow rate and energy

The mass flow rate (m°) and energy concept can be understood from the following logic,

Power = Mass flow rate * Specific work, Power = Energy / time

The above expression can be elaborated below to understand the concept between mass flow rate and energy.

Power = Energy / time    (J/s)

Energy = Power * Time

Another equation of power in terms of the mass flow rate,

Power = Mass flow rate * Specific work

Finally, the energy is,

Energy = Mass flow rate * specific work * time

The unit conversion of energy from the above equation,

The unit of Energy = kg/s * J/kg * s = J

The power can be given in terms of the force and the velocity as below,

P = v * F

Where,

v = Velocity in m/s

F = Force in Newton (N)

The power can be given in terms of the torque and the angular velocity as below,

P = τ * ω

Where,

τ = Torque in Newton * meter (N * m)

ω = Angular velocity in Rad/s

The conservation of the energy principle on control volume is explained as below.

Heat energy – Work energy + Energy entering the system of control volume – Energy leaving the system of the control volume = Net energy change (Control volume)

Two types of power can be separated from this principle on control volume.

• Heat power
• Work power

The above both power can be expressed as below,

Heat power = m° * q

Work power = m° * w

The control volume’s total power is the difference between heat and mass entering the system and work and mass leaving the system.

Total Power = (Heat power + m° e1) – (Work power + m° e2)

Heat power – work power = m° * Δe

The development of the power equation is more straightforward than the energy equation as per the Principle of conservation of energy

Deepakkumar Jani

I am Deepak Kumar Jani, Pursuing PhD in Mechanical- Renewable energy. I have five years of teaching and two-year research experience. My subject area of interest are thermal engineering, automobile engineering, Mechanical measurement, Engineering Drawing, Fluid mechanics etc. I have filed a patent on "Hybridization of green energy for power production". I have published 17 research papers and two books. I am glad to be part of Lambdageeks and would like to present some of my expertise in a simplistic way with the readers. Apart from academics and research, I like wandering in nature, capturing nature and creating awareness about nature among people. Let's connect through LinkedIn - https://www.linkedin.com/in/jani-deepak-b0558748/. Also refer my You-tube Channel regarding “Invitation from Nature”