Pressure and flow rate are two crucial concepts in fluid mechanics, closely related to each other. In fluid mechanics, pressure is the force per unit area, while flow rate is the velocity of a fluid passing through an area per unit time. The Bernoulli and Poiseuille equations commonly demonstrate the relationship between flow rate and pressure.
Let’s explore the relationship between pressure and flow rate in more detail.
What is Pipe Flow Rate?
Pipe flow rate is the speed at which a fluid flows through a pipe, usually expressed in meters per second (m/s). Selecting the correct pipe flow rate is crucial to system design. It affects pressure loss, energy consumption, conveying capacity and piping economics.
The flow rate (v) can be calculated by using the formula for flow rate (Q) and pipe cross-sectional area (A): v = Q / A . When the flow rate is constant, choosing a larger pipe diameter will reduce the flow rate, thus reducing the head loss and pump head. Conversely, smaller pipe diameters increase the flow rate, increasing resistance and operating costs.
What is Pipe Pressure?
Pipe pressure is the force exerted on the pipe wall by the fluid inside the pipe. It is usually expressed in terms of force per unit area, and the international unit is Pascal (Pa), which is commonly used in engineering as MPa or bar.
According to different situations, pipeline pressure can be divided into the following categories:
Static pressure: pressure that does not change with time, or pressure that changes slowly with time.
Dynamic pressure: It is the pressure that changes rapidly with time, i.e. the dynamic pressure is the amount of kinetic energy per unit volume of fluid. Usually calculated using 1/2ρν2. Where ρ – fluid density; v – velocity of fluid motion.”
Total pressure: Also known as full pressure or stagnation pressure. Moving fluid isentropic stagnation pressure. In the incompressible fluid flow, the total pressure is equal to the sum of static pressure and dynamic pressure.
Absolute pressure: Absolute pressure is a pressure measurement relative to a complete vacuum. It directly reflects the absolute value of the pressure, including the entire pressure, including atmospheric pressure.
Gauge pressure: Pressure measurement relative to local atmospheric pressure. It tells us how much the measured pressure is higher or lower than the atmospheric pressure.
Differential pressure: The relative difference between two pressures.
Pressure Equation
The pressure equation is the force per unit area, usually expressed as P in pascals. The formula is as follows:
P = F / A
where: F is the force and A is the area.
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How Many Factors Affect Flow Rate?
The flow rate of a pipe can be affected by some factors, which are described in detail below:
Pipe cross-sectional area
At a fixed flow rate, the cross-sectional area of a pipe is inversely proportional to the flow rate. The smaller the pipe cross-section, the higher the flow rate.
Fluid Flow
At a constant pipe cross-sectional area, the fluid flow is directly proportional to the flow rate. The higher the flow rate, the greater the flow velocity.
The difference in pressure between the two ends of a pipe indicates that the greater the pressure difference, the greater the flow rate.
Pipe Length and Friction Coefficient
An increase in pipe length or an increase in the friction coefficient results in a decrease in flow rate when the head loss along the pipe is constant.
Physical Properties of Fluids
Effect of Density: Density affects the flow rate. For a given pressure difference, the higher the density, the lower the flow rate.
Influence of viscosity: High viscosity fluids flow in the pipeline will produce greater resistance, thus reducing the flow rate.
Roughness inside the pipe
The rougher the inside of the pipe, the greater the resistance to fluid flow. Rough pipe surfaces cause more friction and swirls in the fluid, which reduces the flow rate.
Key Equation of Flow Rate and Pressure
First of all, the formula for calculating the flow rate of the pipeline is: Q = A ×V× 3600
where Q is the flow rate (unit: m3/hour). A is the cross-sectional area of the pipeline (unit: square meter). V is the flow rate (unit: m/s)
The formula for the relationship between pressure and flow is basic in fluid mechanics, also known as Bernoulli’s theorem. Its basic idea is that there is a relationship between the velocity and pressure of a fluid at different locations. When a fluid passes through a section of pipe, its velocity and pressure change.
When the fluid flows horizontally, the height h remains constant, i.e., h1=h2. At this point, Bernoulli’s equation is simplified to Bernoulli’s theorem formula as follows:
From the equation of Bernoulli’s theorem, it can be seen that when the fluid velocity increases, the pressure decreases and the flow rate increases. Conversely, when the fluid velocity decreases, the pressure increases and the flow rate decreases. Therefore, the relationship between pressure and flow is inversely proportional.
Poiseuille’s Law for Viscous Fluids
Poiseuille’s law focuses on viscous fluids in pipes, while Bernoulli’s equation applies to ideal fluids. The equation is as follows:
Q=πr4xΔP/8ηl
Q represents the volumetric flow rate. P₁, P₂ are the pressures at the ends of the pipe. r is the radius of the pipe, μ is the viscosity of the fluid. L is the length of the pipe.
Poiseuille’s law shows that there is a significant quadratic relationship between the pipe and the radius. A pipe with a radius twice the radius can increase its flow rate by a factor of about 16. The law also shows that the greater the differential pressure, the greater the flow rate.
The law is only valid under certain conditions, including laminar (non-turbulent) flow, incompressible Newtonian fluids, and long, straight pipes.
Flow and Pressure Relationship Formula Example
Example 1: Gas Flow Rate and Pressure Relationship Formula
Stainless steel seamless pipe φ25.4×1.65, the working medium is nitrogen N2, the working pressure P = 0.8MPa, the working temperature t = 20 ℃ for the working condition flow Q?
Solution: take a cross-section of the stainless steel pipe as a reference surface, then the medium in 1h to stay in the cross-section of the pipeline through the flow of:
Q = V πR² x 3600
where,
Q: working condition flow rate – m³
V: media flow rate – m / s:
R pipeline radius – m
So we get the following flow rate calculation formula :
In the actual engineering applications, the flow rate (V) in the pipeline is affected by many factors (use pressure, pipe diameter, use flow rate, etc.), so the reasonable flow rate should be decided based on economic trade-offs to decide.
General liquid flow rate of 0.5 ~ 3m / s, gas flow rate of 10 ~ 30m / s. Now, 0.8MPa case we take: flow rate V = 10m / s, the pipe diameter of 22.1mm in the working conditions of the hourly flow:
Example 2: Water Flow Rate and Pressure Relationship Formula
When the medium is water, the known pipe diameter and flow rate to find the flow.
conditions: pipe diameter= 100mm = 0.1m, flow rate = 2m/s.
calculation:
- cross-sectional area A = π × 0.1²/4 ≈ 0.00785m ²
- Q = 2 × 0.00785≈ 0.0157m²/s = 56.52m²/h.
If you need to calculate the relationship between flow rate and pressure, then I recommend you use calculator 1 and calculator 2.
Mass Flow Rate And Pressure Relationship Formula:
The above discussion is all about the relationship between volumetric flow rate and pressure. If you need to convert the mass flow rate, then use the Volume Flow Rate ✖ Density.
What is a Pressure Drop?
There are 2 types of pipe pressure loss:
1. Along the course of the pressure loss is the liquid in the flow process to overcome the energy lost along the resistance. Including friction pressure loss and additional friction pressure loss caused by the flow.
2. Local pressure loss is the liquid in the flow process used to overcome the local resistance loss of energy. Including the friction pressure loss of the shaped pipe fittings themselves and the pressure loss caused by eddy current.
Solution:
1. Select a reasonable workpiece flow rate. From the calculation of fluid resistance, loss can be seen, whether along the resistance or local resistance is proportional to the flow rate squared; the flow rate is high, the pressure loss is large. But the flow rate is low, consuming more metal materials. Therefore, it must be economically comparable, and the choice of a reasonable workpiece flow rate.
2. Minimize the connectors and accessories in the pipeline.
3. Keep the integrity of the valve in the piping system.
4. should be as short as possible to shorten the total length of the pipeline.
What is a Turbulence Problem?
In the pipeline, when the flow rate increases to a certain degree, the originally smooth laminar flow will suddenly become turbulent, fluid particles begin to collide around, and the trajectory becomes elusive.
Common solutions:
- Change the pipe design and geometry.
- Control fluid flow parameters.
- Use additives.
- Improve fluid condition.
- Increase maintenance.
- Use active control techniques.
- Apply special wall structure.
Can you have high pressure but low flow rate?
In fluid dynamics, it is indeed possible to have high pressure but low flow rate. This is often the case in applications where high pressure is needed to overcome resistance or to push a fluid through a narrow channel. In hydraulics, for example, the use of multistage pumps can produce high pressure while maintaining a low flow rate. Multi-stage pumps are pressurized in stages by means of multiple impellers, which allows for a significant increase in outlet pressure without increasing the flow rate.
What is the relationship between hydraulic pressure and flow?
Hydraulic pressure has nothing to do with flow rate; it is related to the pressure difference between the two ends of the pipeline and also related to the density and viscosity of the medium in the pipeline. What is the relationship between hydraulic pressure and flow? Static pressure has nothing to do with flow; it has to do with the pressure difference between the two ends of the pipe, and it has to do with the density and viscosity of the medium in the pipe.
Can you increase the flow rate without increasing the pressure?
Of course, besides increasing pressure can increase the flow rate, we have other ways to increase the flow rate. Here are the details:
1. Adjust the flow rate of the fluid: the flow rate is inversely proportional to the flow rate of the fluid, that is, the larger the flow rate of the fluid, the smaller the flow rate. The smaller the flow rate of the fluid, the larger the flow rate. By changing the flow rate of water supply or air supply, the flow rate can be changed.
2. Change the diameter of the pipe: According to the continuity equation, the flow rate in the pipe is inversely proportional to the diameter of the pipe. When the diameter of the pipe decreases, the flow rate increases. When the diameter of the pipe increases, the flow rate decreases.
3. Installation of throttling devices: By installing throttling devices in the pipeline, such as orifice plates, nozzles, throttling valves, etc., so as to change the flow rate.
4. Change the viscosity of the fluid: the greater the viscosity of the fluid, the smaller the flow rate. The smaller the viscosity of the fluid, the larger the flow rate. By changing the temperature of the fluid or adding specific substances, the viscosity of the fluid can be changed, thus changing the flow rate.
5. Use of external forces: Applying external forces, such as wind, turbines, pumps, etc., can accelerate or slow down the flow rate of the fluid.
In short, the relationship between flow rate and pressure is very complex. We hope that you can have a detailed understanding of their relationship after reading the above text.
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