Understanding The Relationship Between Flow And Pressure

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Once a piping system is confirmed, the flow rate is directly related to the square root of the piping system’s pressure difference; the greater the difference in pressure, the greater the rate of flow. If a man-made pressure loss system such as a regulating valve is installed in the piping system, the effective pressure difference is reduced, thus reducing the flow rate. 

When working with piping systems, a common question is if the flow rate is proportional to the pressure, and how they are related. Pressure and water flow are the two components that power plumbing systems. 

Plumbing and piping systems completely depend on the water flow and pressure. For example, if the water pressure is too high or too low in your plumbing system, it can damage equipment such as pipes and fixtures. 

Flow rate is the amount of fluid that moves through an open channel or closed pipe, and the pressure is the internal pressure inside the pipe. The greater the differential pressure, the higher the flow rate is. 

To understand the relationship between flow and pressure, you need to understand what flow and pressure are, how to work out the flow rate from the differential pressure, and what flow meters are used. 

What Is Flow?

In plumbing systems, flow is the amount of water to pass through a pipe at any given time. The water flow in plumbing is determined by the pipe width and the pressure. To put it into perspective, smaller pipes supply water to plumbing systems at a lower flow rate than larger pipes.

The pressure also affects the flow rate. The greater the water pressure, the greater the water flow rate. So, the larger the plumbing system, the harder it is for the pressure to be dispersed evenly, and so the water flow rate will be lower. This is known as the flow rate and differential pressure. 

What Is Pressure?

The general term “pressure” is the continuous physical force exerted against or on a contacted object. But, water pressure is the force exerted on the water to push it through a piping system or larger plumbing application.

Water pressure is affected by altitude and gravity. Water is a denser substance than atmospheric air, so the position and height can change the water pressure. The higher the water source, the greater the pressure. Gravitational force also affects water pressure. 

Does Pressure Affect Flow Rates?

Yes. As there is a very close relationship between water flow and pressure, an increase in pressure also increases the flow rate. Therefore, changes in the pressure will directly change the flow rate.

Why Are Flow And Pressure Important?

Monitoring flow and pressure are essential in the following applications:

  • Monitoring and controlling water in taps
  • Dosing chemicals to water treatment systems
  • Leakage detection and reduction
  • Monitoring water consumption in commercial and residential buildings 
  • Monitoring discharge water and influent water quantity
  • Monitoring the flow of water between reservoirs

Pipe Pressure Types

Pressure is the force that pushes the water through the pipe, which measures the pressure from the inlet to the outlet of the pipe. 

There are three types of pipe pressure that you need to know.

The first one is the pressure source to the destination. This pressure is the force required to push the fluid through a piping system. An example of this is pushing fluid into a pressurized tank from a pipe or a hydraulic system. 

Next is pressure and head. As you push fluid from a high to a low elevation, the pressure increases. The higher the elevation or the heavier the fluid, the greater the pressure at the pump. You can feel this pressure when you swim to the deep end of a swimming pool, or if your tap water comes from an elevated water tank. 

Lastly, is pressure due to friction. This pressure is the largest contributor to pump systems. When friction increases inside the pipe, the pressure and flow are decreased. A frictional loss occurs due to the fluid passing through downstream equipment. When the pump speeds up, the flow increases, and so does the pressure. 

Relationship Between Pipe Diameter Pressure And Flow

The pipe diameter takes into account the thickness of the pipe wall. The pipe’s outer and inner diameters, typically have the same thickness, so the pipe diameter is taken from the inner and outer average. 

Pressure refers to the internal pressure of the fluid inside the pipe. The flow rate is also known as instantaneous flow; the amount of fluid that flows through the pipe (it can be closed or an open channel) per unit of time. The amount of fluid that passed through the pipe is called volumetric flow when the fluid is expressed in volume. 

Most piping systems use a pipe diameter of 15-22mm*. The smaller the pipe diameter, the less water can travel through the pipe. An increase in friction occurs when the pipe gets smaller, so the pressure decreases.

*Make sure the pipe is adequately sized to allow the flow without exceeding the pressure rating of the pump and system. 

How Are Flow And Pressure Related?

The flow rate is not determined by the rate of flow or pressure in the pipe, but by the pressure drop gradient along the pipe. So, to work out the flow, the length of the pipe and the differential pressure at both ends give the flow rate and the flow rate inside the pipe. 

From the perspective of qualitative analysis, the relationship between the pressure in the pipe and the flow rate is directly proportional; the greater the pressure, the higher the flow rate.

The calculation looks like this: 

Flow rate = flow rate x pipe inside diameter (ID) x pipe ID x π ÷ 4

When calculating the flow rate, we take the measurement at one end. After all, the pressure only comes from one end of the pipe because the flow of fluid inside a pipe is unidirectional. When the outlet is closed, the fluid cannot pass through the pipe. 

When the pipe valve is open, the pressure drops, and then the pump kicks in and the pressure climbs. The fluid then flows depending on the pressure inside the pipe. When the valve is closed, there is no flow, and the pressure climbs. 

To understand quantitative analysis, we use hydraulic model experiments. These can be done in your home or at work. All you need is to install a pressure gauge and a flow meter

Pressure pipe flow can be measured by following these steps:

  1. Calculate the resistivity of the pipe (s). The resistivity of the pipe can be calculated using the Sheverev formula s=0.001736/d^5.3 
  2. Calculate the working head difference at both ends using the following calculation: H = P/(ρg). If the pipe has a horizontal drop (h), use the calculation: H=P/(ρg)+h
  3. Calculate the flow rate (Q) using the following equation: Q = (H/sL)^(1/2)
  4. Flow velocity V = 4Q/(3.1416 * d^2)

Where:

  • P = The pressure difference between the two pipe ends (measured in Pa – pascal)
  • H = The difference in head between the two pipe ends (measured in m – meter)
  • L = The length of the pipe (measured in m)
  • Q = The flow rate (m3/s) 
  • p =  The pressure in the fluid
  • g = The acceleration of gravity
  • ρ = The density of the fluid

Another method to measure the flow is to time yourself filling a bucket with water. This method is commonly used to measure water flow at a faucet or shower.

  1. Firstly, turn off the water.
  2. With a stopwatch or phone timer, time how long it takes for the tap to fill a container – measure this in seconds.
  3. Divide 60 by the number of seconds from step 2. For example, if it took 20 seconds to fill the container, then: 60 / 20 = 3 gallons per minute. 
  4. This gives you the flow rate of the tap (or application being measured) in gallons per minute.

Flow And Pressure: Bernoulli’s Equation

When talking about pressure and flow, it’s not long before Bernoulli’s equation is mentioned. 

Bernoulli’s principle came from Daniel Bernoulli in 1726 when he stated: “In a current or stream, if the velocity is low, the pressure is high. If the velocity is high, the pressure is low”. 

Referring to hydrodynamics, Bernoulli’s principle is used in fluid mechanics, and it is the essence of fluid mechanical energy. As Bernoulli’s equation was concluded from the conservation of mechanical energy, it can only be used to work out the flow and pressure of incompressible fluids. 

Bernoulli’s principle uses the following equation: p+1/2ρv2+ρgh=C

Where:

  • p = The pressure in the fluid
  • v =  The fluid’s flow velocity 
  • ρ = The density of the fluid
  • g = The acceleration of gravity
  • h = The height of the point/horizontal drop
  • C = The constant

For Bernoulli’s principle to work, the following assumptions must be satisfied:

  1. There should be a steady-state flow (the fluid’s properties do not change over time).
  2. There should be an incompressible flow (the density must be constant).
  3. There should be frictionless flow.
  4. The fluid should flow along the streamline, and the flow lines must not intersect.

What Is A Pressure Drop?

A pressure drop also referred to as a pressure loss, helps to determine the size of the pumps or motors needed in the piping system. It also allows you to work out the pipe diameter required to move the fluid through the piping system.

The greater the pressure drop in the pipe, the more energy is consumed to maintain a constant flow. Therefore, requires a more powerful motor.

On the other hand, the lower the pressure drop in the piping system, the less energy is used, and therefore, less power is needed from a motor. 

The pressure drop also plays a key role in the type of pressure pump head required in the piping system. The pressure pump measures the force the pump applies to move the fluid. If a large pressure drop occurs, the pressure head will be larger to overcome the drop, which can have adverse effects on the piping system. Issues with large pressure heads include premature failure of seals and possible over-pressure faults in the piping system.

What Affects The Pressure Drop?

  • The product being pumped through the piping system
  • The mechanical components in the piping system
  • A change in the elevation of the piping system

Relationship Between Flow Rate And Pressure Drop

The pressure drop is dependent on the flow rate, and vice versa. So if the flow rate is higher, the greater the pressure drop will be. Alternatively, if the flow rate is lower, the pressure drop will also be lower.

Pressure Vs Flow Rate Chart

If you are not quite a mathematician, a flow and pressure calculator can be used to calculate the average flow rate of water based on the length and diameter of the pipe. 

As previously mentioned, the relation between the flow and the pressure is directly proportional. So, as pressure increases, the flow rate increases. This can be seen in a pressure and flow rate chart

Converting Flow Rate To Pressure

To convert the flow rate to pressure:

  • Calculate the square root of the volumetric flow rate
  • Calculate the square root of the flow factor
  • Divide the square root of the volumetric flow rate by the square root of the flow factor
  • Multiply the result with the specific gravity of the fluid passing through the system – this will give you the differential pressure

Measuring Flow And Pressure 

Whether you are monitoring the water flow in a hydroponics system or a large plumbing system, a flow meter is required to measure flow and a pressure sensor* to measure the pressure. 

Flow meters accurately measure the flow rate and the amount of water that is flowing through a pipe. For accurate flow monitoring, both a precision flow meter and a well-designed flow meter totalizer are required. 

*If you are unsure which pressure sensor your application requires, read out guide on the 7 types of pressure sensors

Summary

Fluid passing through a system requires a pressure gradient between two points, such as the inlet and outlet. Within the system, flow is directly proportional to the pressure. So, when high pressure happens, it drives a greater flow rate compared to lower pressures. 

If you have any questions regarding flow or pressure, or what flow meter/pressure sensor will best suit your needs, do not hesitate to contact our world-class team at Atlas Scientific

Pressure Sensors

Flow Meters

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