Are the flow rate and pressure in the pipeline proportional? Is the flow rate related to pressure, flow rate, and pipe diameter? From the perspective of qualitative analysis, the relationship between pressure and flow in the pipeline is proportional. That is, the greater the pressure, the greater the flow rate. The flow rate is equal to the velocity multiplied by the section. For any section of the pipeline, the pressure comes from only one end, that is, the direction is one-way. When the outlet is closed (the valve is closed), the fluid in the pipe is in a prohibited state. Once the outlet is opened, its flow rate depends on the pressure in the pipe.

## Pipe Diameter vs Pressure vs Flow

The pipe diameter means that when the pipe wall is relatively thin, the outside diameter of the pipe is almost the same as the inside diameter of the pipe, so the average value of the outside diameter of the pipe and the inside diameter of the pipe is taken as the pipe diameter. Usually refers to the general synthetic material or metallic pipe, and when the inner diameter is large, the average value of the inner diameter and the outer diameter is taken as the pipe diameter. Based on the metric system (mm), it is called DN (metric unit).

Pressure refers to the internal pressure of the fluid pipe.

Flow refers to the amount of fluid flowing through the effective cross-section of a closed pipeline or open channel per unit time, also known as instantaneous flow. When the amount of fluid is expressed by volume, it is called volume flow. When the amount of fluid is expressed by mass, it is called mass flow. The volume of fluid flowing through a certain section of pipe per unit time is called the volume flow rate of the cross-section.

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## flow rate and pressure relationship

First of all, flow = flow rate × pipe inner diameter × pipe inner diameter × π÷4. Therefore, the flow rate and the flow rate basically know one to calculate the other parameter.

But if the pipe diameter D and the pressure P in the pipe are known, can the flow rate be calculated?

The answer is: It is not yet possible to find the flow velocity and flow rate of the fluid in the pipeline.

You imagine that there is a valve at the end of the pipe. When closed, there is pressure P in the tube. The flow rate in the tube is zero.

Therefore: The flow rate in the pipe is not determined by the pressure in the pipe, but by the pressure drop gradient along the pipe. Therefore, it is necessary to indicate the length of the pipeline and the pressure difference between the two ends of the pipeline in order to find the flow rate and flow rate of the pipeline.

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If you look at it from a qualitative analysis point of view. The relationship between pressure and flow in the pipeline is proportional. That is, the greater the pressure, the greater the flow rate. The flow rate is equal to the velocity multiplied by the section.

For any section of the pipeline, the pressure comes from only one end. That is to say, the direction is one-way. When the outlet in the pressure direction is closed (valve closed). The fluid in the tube is prohibited. Once the exit opens. Its flow rate depends on the pressure in the pipeline.

For quantitative analysis, you can use hydraulic model experiments. Install pressure gauges, flow meters, or measure flow-through capacity. For pressure pipe flow, it can also be calculated. The calculation steps are as follows:

- Calculate the specific resistance S of the pipeline. If it is an old cast iron pipe or old steel pipe. The specific resistance of the pipeline can be calculated by Sheverev formula s=0.001736/d^5.3 or s=10.3n2/d^5.33. Or check the relevant form;
- Determine the working head difference H=P/(ρg) at both ends of the pipeline. If there is a horizontal drop h (referring to the beginning of the pipe higher than the end by h).

Then H=P/(ρg)+h

In the formula: H: take m as the unit;

P: is the pressure difference between the two ends of the pipe (not the pressure of a certain section).

P is in Pa; - Calculate the flow rate Q: Q = (H/sL)^(1/2)
- Flow rate V=4Q/(3.1416 * d^2)
- In the formula: Q —— flow rate in m^3/s;
- H —— The head difference between the beginning and the end of the pipeline, in m;
- L —— The length from the beginning to the end of the pipe, in m.

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## Flow Rate and Pressure Formula

Mention pressure and flow rate. I think many people will think of **Bernoulli’s equation**.

Daniel Bernoulli first proposed in 1726: “In water or air currents, if the velocity is low, the pressure is high. If the velocity is high, the pressure is small”. We call it “Bernoulli’s Principle”.

This is the basic principle of hydraulics before the continuum theory equation of fluid mechanics is established. Its essence is the conservation of fluid mechanical energy. That is: kinetic energy + gravitational potential energy + pressure potential energy = constant.

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Have to be aware of it. Because the Bernoulli equation is derived from the conservation of mechanical energy. Therefore, it is only suitable for ideal fluids with negligible viscosity and incompressible.

Bernoulli’s principle is often expressed as:

This formula is called Bernoulli’s equation.

Where

p is the pressure of a certain point in the fluid;

v is the flow velocity of the fluid at that point;

ρ is fluid density;

g is the acceleration of gravity;

h is the height of the point;

C is a constant.

It can also be expressed as:

Assumptions:

To use Bernoulli’s law, the following assumptions must be met before it can be used. If the following assumptions are not fully met, the solution sought is also an approximation.

- Steady flow: In a flow system, the nature of the fluid at any point does not change with time.
- Incompressible flow: the density is constant, when the fluid is a gas, the Mach number (Ma)<0.3 is applicable.
- Friction-free flow: The friction effect is negligible, and the viscous effect is neglected.
- Fluid flows along streamlines: fluid elements flow along streamlines. The streamlines do not intersect each other.

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