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Flow Rate Formula

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Last updated date: 17th Apr 2024
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What is a Flow Rate?

The amount of fluid (water flow rate formula) moving through any position through a region during a period of time is known as the volume flow rate Q. The volume flow rate formula can be written in symbols as:

Q = \[\frac{V}{T}\]

where V denotes volume and t denotes time. The SI unit for the flow rate is m/s, although there are many other units for Q in general use. A sleeping adult's pulse, for example, pumps blood at a rate of 5.00 litres per minute. A litre (L) is equal to 1/1000 of a cubic meter or 1000 cubic centimetres. Flow rate and velocity are two physical quantities that are related but not identical. Consider the flow velocity of a river to help you understand the difference. The river's flow rate increases as the velocity of the stream increases. However, the scale of the river has an effect on the flow rate.

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Q = A\[\bar{v}\] is the same relationship between flow rate Q and velocity \[\bar{v}\], where \[\bar{v}\] is the average velocity, and A is the cross-sectional area.

The method for obtaining this relationship is seen in the above figure. The volume V = Ad of the shaded cylinder flows past the point P in time t. 

The following is obtained by multiplying both sides of this relationship by t:

\[\frac{V}{t}\] = \[\frac{Ad}{t}\]

We know that Q = \[\frac{V}{T}\] and the average speed is denoted by \[\bar{v}\] = \[\frac{d}{t}\],

Therefore, 

Q = A\[\bar{v}\]


Mass Flow Rate Formula

The conservation of mass is a basic physics principle. The sum of mass in certain problem domains remains stable — mass is neither produced nor lost. The mass of every object is equal to the volume of the object multiplied by its density. The density, volume, and shape of a fluid (a liquid or a gas) will all vary with time within the domain. Furthermore, the mass will shift inside the domain. A gas flow into a constricted tube is depicted in the diagram. There is no mass deposition or destruction in the tunnel; the same volume of mass reaches and exits the tube. The same volume of mass flows through the tube in every plane perpendicular to the middle line. The mass flow rate formula is the volume of mass that passes through a plane. The principle of mass conservation (continuity) states that the mass flow rate equation into a conduit is constant. The mass flow rate can be calculated using the flow conditions.

The mass flow rate equation formula is given by,

\[\dot{m}\] = \[\frac{dm}{dt}\]


IV Flow Rate Formula

The drop factor is used to measure the drops per minute. The IV flow rate (drip rate) is calculated using expression given by the following formula: total volume (in mL) divided by time (in min), multiplied by the drop factor (in gtts/mL), equals IV flow rate in gtts/min.


$IV\: flow\: rate= \dfrac{Volume}{time}\times drop\: factor$


Air Flow Rate Formula

Using the continuity equation for gases, you can measure air flow patterns in various parts of a pipe or hose system. Both liquids and gases are considered fluids. The mass of air entering a straight and sealed pipe system equals the mass of air exiting the pipe system,  as per the continuity equation. 


Calculation of Flow Rate Using Pressure

How to Calculate Flow Rate from Pressure?

We use Bernoulli’s theorem to calculate the differential pressure measurement for different flows.


To begin, we must first understand fluid dynamics, or more specifically, Bernouilli's concepts – the physics behind the differential pressure flow meter. Bernoulli was a Swiss mathematician who studied energy conservation in the 1700s. In a nutshell, the theory named after him states that the number of all energies – static, potential, and kinetic – in a fluid flowing through a pipe stays constant within the pipe.


The sum of all these energies upstream equals the energies downstream for a differential pressure meter. Static energy is represented by pressure, potential energy by height, and kinetic energy by velocity.


Solved Examples

1. What is a material's mass flow rate if 20 ml of it is obtained in 20 seconds? The substance has a density of 0.5 gm/ml.

  1. 0.5

  2. 0.1

  3. 0.2

  4. 1

Solution:

We know, Mass flow rate= Mass/Time

Mass= Volume x Density

Mass=20 x 0.5= 10

Mass flow rate= 10/20=0.5

Answer: a) 0.5


2. 100 grams of liquid is obtained in 10 seconds at what mass flow rate of the liquid passing through a pipe?

Solution: 

Let us convert 100 grams in terms of kilograms, we get,

Mass = 0.1kg and the time is 10 seconds, 

Therefore, Mass Flow Rate = \[\frac{0.1}{10}\] = 0.01 Kg/s 



Conclusion

In this topic we understood the meaning of flow rate, types of flow rate and how to calculate different types of flow rate. It is very important to understand this concept because it is widely used in Fluid Dynamics and helps a lot while applying Bernoulli’s Theorem.  Bernoulli’s theorem is used to calculate the pressure difference for different types of flows.

FAQs on Flow Rate Formula

1. What is Bernoulli’ s Principle?

Bernoulli’s equation relates the pressure, flow speed and height for flow of an ideal (incompressible and non-viscous) fluid. The pressure of a fluid depends on height in the static situation and it also depends on the speed of flow.

2. Define Principle of Continuity.

It states that, when an incompressible and non-viscous liquid flows in a streamlined motion through a tube of non-uniform cross-section, then the product of the area of cross section and the velocity of flow is same at every point in the tube.

3. How is flow rate related to the Principle of Continuity?

Principle of Continuity is based on the mass flow rate of the fluid as when the liquids are assumed to be incompressible, the rate of flow entering into an area must equal the rate of flow coming  out of an area. This is known as the equation of continuity.