In the article we will discuss about the topic of “Volumetric flow rate with pressure” and their related facts and their relationship which is applied in the field of engineering.

**In the piping system the pressure related to the inside net force which is applied perpendicular to the axis of the pipe or the channel and volumetric flow rate means the inside condition related to the volume of the liquid substance in the pipe or channel** **where the force is applied parallel to the pipe or the channel of the piping system. For the both condition the force is applied from the external to the object.**

**Volumetric flow rate:**

In the system of the piping the volumetric flow rate is a very important factor. By the help of the volumetric flow rate we could easily summarize the inside condition of the piping system.

**In the inside condition of a pipe or a channel, the volume of the liquid substance is moving at a cross sectional area of the pipe or channel in a particular given time period at some standard condition where the temperature and pressure is remains unchanged.**

**Read more about** **Volumetric flow rate:It’s All Important Concept**

**Formula:**

The formula of the volumetric flow rate in piping system is,

Volumetric flow rate = (Flow velocity of the liquid substance) *(Cross sectional area of a pipe or a channel)

The mathematically form of the volumetric flow rate of the piping system is,

Q = vA

Where,

Q = Volumetric flow rate of the liquid substance

v = Velocity of the liquid substance

A = Cross sectional area of a pipe or a channel

In another word we could express that**, **

**The volumetric flow rate is the ratio between the changes of volume with the change in time.**

**Formula:**

The formula of the volumetric flow rate is,

Volumetric flow rate = Change in volume/Change in time

It can be expressed as,

Q = dV/dt

The unit of this parameter is cubic meter per second. The dimension can be written for the volumetric flow rate is, L^{3}T^{-1}.

**Pressure**:

In the S.I. system the parameter of pressure is measured by the units is Newton per square metre, Newton per square millimetre, Meganewton per square metre, kilo Newton per square metre. But sometimes for measuring the bigger amount the bigger pressure or bar is used. The most used unit that is used to measure the pressure is **Pascal**.

**Pressure can be defined for the piping system is the net force perpendicularly applied to the axis of the pipe or the channel in a particular given area at a standard time.**

**Pressure equation:**

The formula of the pressure can be written as,

Pressure = Net force applied / Cross sectional area of the pipe or the channel

The pressure can be mathematically expressed as,

P = F/A

Where,

P = Pressure

F= Net force applied to the pipe or channel

A = Cross sectional area

**1 Pa = 1 N/ square metre and**

**1 kPa = 1 KN/square metre**

**Volume flow rate pressure relationship:**

In an open system when the liquid substance is moved in a motion from one place to another place in a given particular area at a fixed temperature. If that time the net force is applied parallel axis to the pipe or the channel pressure is produced.

**The volumetric flow rate pressure relationship can be written as,**

F = Q/t

**Where, F = Flow of the liquid substance**

**Q = Quantity of the flowing liquid substance in the piping system**

**t = Taken time to flow**

The relation between the volumetric flow rate and the pressure is **directly proportional**. Means increasing the pressure the more volumetric flow rate as well as decreasing the pressure means less amount of volumetric flow rate arise.

Flow can be categorized with pressure in two types,

**Laminar flow**

**Turbulent flow**

**Laminar flow:**

Laminar flow can be defined as the particles which are present in the liquid substance are going through in a defined path at a specified area and under some standard condition.

**Turbulent flow:**

Turbulent flow can be defined as the particles which are present in the liquid substance are going through not in a defined path and the particles are crosses to each other at a specified area and under some standard condition.

**Volumetric flow rate equation with pressure:**

The topic of volumetric flow rate equation with pressure we get a very clear concept from the Bernoulli’s equation.

**Bernoulli’s equation**: When the incompressible liquid substance is flow in a defined path in a particular area at a fixed time the particle of the liquid substance containing the energy is remain constant.

The mathematical expression for the **Bernoulli’s equation is given below,**

The eqn (1) only applied for the ideal incompressible liquid substance.

h_{L} = Loss of energy in the sections between 1 and 2.

The eqn(2) is applicable for the real liquid substance.

**Calculate volume flow rate with pressure:**

Now we will understand this topic with the help of some problems.

**Problem**: **Soumen have a hobby of gardening. He daily gives water to his garden by the water pipe with is attached to his houses pipeline. The volume rate of the pipe by which he gives water is 40 cubic meters per second. The diameter of the pipe is 5 meter .Now calculate the speed of the pipe.**

**Solution**: Given data are, d = 5 meter, r =5/2 = 2.5 meter.

We know that,

V = Ah = Ad

Δ V = AΔd

Δ V/Δt = AΔd/Δt = A x v

40m^{3}/s = π x (2.5)^{2} x v

[40 = 5 π x v

v = 40/5 x π = 2.54 m/s

So the speed of the pipe is, 2.54 meter per second.

**Volumetric flow rate vs. pressure:**

Here we will discuss about the topic of volumetric flow rate vs. pressure. These both topics are used to understand the internal condition of the piping systems and also help the process to run smoothly.

| Volumetric flow rate | Pressure |

Relation with velocity | The relation between the volumetric flow rate and the velocity is directly proportional. Means if the value of the velocity increases then the value of volumetric flow rate is also increases and if the value of velocity decreases then the value of volumetric flow rate is also decreases in the pipe or a channel. | The relation with the pressure and velocity is directly inversely proportional. Means the value of the velocity is increases then the value of pressure is decreases and if the value of velocity is deceases then the value of pressure is increases in the pipe or the channel of a piping system. |

Classification | The types of the volumetric flow rate is,1.Vortex meter 2.Ultrasonic meter 3.Turbine meter4.Magnetic meter | The types of pressure is, 1.Gauge pressure 2.Absolute pressure 3.Atmospheric pressure4.Sealed pressure or vacuum pressure |

Dimension | The dimension of the flow for liquid is, M^{0}L^{3}T^{-1}. | The dimension of the pressure is, ML^{-1}T^{-2}. |

Inside condition | The volumetric flow rate is mainly used to understand that, how much the volume is present inside of the pipe or channel at a given time. | The pressure means the molecules present inside the pipe. |

Formula | The formula of the volumetric flow rate is, Volumetric flow rate = (Flow velocity of the liquid substance) *(Cross sectional area of a pipe or a channel) | The formula of the pressure is, Pressure = Net force applied / Cross sectional area of the pipe or the channel |

Measuring instruments | The value of the volumetric flow rate is measured by the instruments are,1. Anemometer 2. Electromagnetic 3. Ultrasonic 4. Fluid dynamic 5. Mass flow meter6. Positive displacement flow meter 7. Obstruction type 8. Inferential | The measuring instrument of the pressure is, 1.Manometer 2.Pressure gauge 3.Pressure tube 4.Barometer 5.Micro meter 6.Bourdon gauge 7.Piezometer |

**Read more about Gauge Pressure: Its Important Properties with 30 FAQs**

**Does volumetric flow rate change with pressure?**

The relation between the volumetric flow rate and pressure is inversely proportional. When the liquid substance is pumped in the certain place that time pressure is increases inside of the piping system at that same time the volumetric flow rate decreases.

**Yes, the volumetric flow rate is changed with the pressure.**

**Volumetric flow rate pressure drop:**

In the laminar flow the conditions of volumetric flow rate pressure drop is arise. If the pressure drop is greater than the volumetric flow rate is also greater. The pressure drop and the volumetric flow rate are dependent with each other.

**Volumetric flow rate**: **The volume of the liquid substance in unchanged during the motion.**

Suppose a huge size amount a of physical quantities’ body is changed into a smaller physical quantities’ body, then as a result the quantity of the volume which is present in the new transformed physical body also present in the small portion of the new physical body, if the portions of the bodies are collect all together and then if they are added then the total volume for the body remain same.

**Pressure drop: The pressure drop in a liquid substance can be explain as, the difference between the total pressures with two points, which a fluid is carry as a network.**

Pressure drop or head loss has a relation with the Fanning friction factor f is,

h_{f} = 2f*l/d*v^{2}/g

In an alternative way the pressure drop can be written as,

P=2f*L/D*ρV^{2}