In water flowing pipeline, pipe size and water pressure are dependent on each other. Because if a pipe’s diameter decreases, the pressure in the pipeline will increase. As per Bernoulli’s theorem, pressure can be reduced when the area of conveyance is reduced. In the narrower pipe, the velocity can be high; hence the pressure will be lower.
If a liquid is passing through a pipe and the diameter of the pipe decreases, then the velocity of the fluid rises, the pressure reduces, and the mass flow remains consistent for a period of time till air density is consistent.
Formulas for flow and pressure (Bernoulli’s equation)
Bernoulli proposed in 1972 – “In a current or stream, if the velocity is low, the pressure is high, the pressure is low when the velocity is high.”
This was the fundamental principle of hydrodynamics before the development of the equations of fluid mechanics and continuous medium theory. Its essence is fluid mechanical energy conservation.
It is critical to know Bernoulli’s equation is derived from mechanical energy conservation. As a result, it applies only to ideal fluids with negligible viscosity and incompressibility.
Bernoulli’s principle is typically stated as follows.
p+1/2ρv2+ρgh=C
This equation is called Bernoulli’s equation.
where
 p is the pressure at a point in the fluid.
 v is the flow velocity of the fluid at that point.
 ρ is the density of the fluid.
 g is the acceleration of gravity.
 h is the height of the point.
 C is a constant.
It can also be expressed as.
p1+1/2ρv12+ρgh1=p2+1/2ρv22+ρgh2
Required Conditions
The solution sought is also an approximation if the following conditions are not fully satisfied.

Steadystate flow
In a flow system, the fluid properties at any point do not change over time.

Incompressible flow
The density is constant, and the Mach number (Ma) 0.3 applies when the fluid is a gas.

Frictionless flow
The friction effect is negligible, as is the viscous effect.

The flow of fluid elements along the streamline
Fluid elements flow along the streamline. The flow lines do not cross.
The Poiseuille’s Law
Flow rate vs pipe size
Poiseuille’s law states that the flow rate through a length of pipe varies with the fourth power of the radius of the pipe. The length of the pipe, the viscosity of the liquid, and the pressure to which the liquid is subjected are all variables that affect the flow rate. Poiseuille’s law assumes laminar flow, which is an idealization that only applies at low pressures and small pipe diameters. Most realworld applications include turbulence.
The law is expressed as:
Volume flow rate = π X pressure difference X pipe radius 4 X liquid viscosity / 8 X viscosity X pipe length.
F = πPr4 / 8nl
To put it another way, at a given temperature, the flow rate through a tube or pipe is inversely proportional to the length of the tube and the viscosity of the liquid. The flow rate is proportional to the pipe pressure gradient and the fourth power of the pipe radius.
Other factors
The pipe diameter vs flow rate:
In a fluid passing through a pipe, a reduction in the diameter of the pipe can compress the flowing fluid. It flows faster, which increases the flow rate. And if the diameter increases, then the flow rate reduces.
The pipe size and flow:
The water pipe pressure remains the same on both facets of the segment of the pipe. The water flow is slower in the bigger pipes, but water pressure in the pipe will increase. In pipes with a small size, water flow is faster as compared to bigger pipes.
The pipe size and water pressure:
The pipe’s diameter decreases, the velocity of the fluid rises, and the pressure decreases. The variations in pipe diameter will not affect the static pressure. When the connection is open, the water pressure moderately decreases. The larger pipe offers minimum resistance to flow, and hence the water pressure in the pipe decreases.
Pipe length and water pressure:
The reduction in pipe length offers resistance against the flow and results in pressure loss. When the flow velocity increases, the pressure decreases, and efficiency reduces.
Flow rate and water pressure:
The pressure affects the flow rate. If the pressure in pipes increases, then the flow rate increases. This equation varies by varying pressure or flow rate and remains constant when these factors remain constant.
Can Pipe Material Affect the Pressure?
Yes, the material of a pipe can affect the pressure in a pipe. The strength and durability of pipes are essential in determining the stress they can take, and stainless steel pipe is generally considered a good choice for highpressure applications. Stainless steel is a strong and durable material that can withstand high pressure without deforming or breaking. However, other materials, such as plastic or aluminium, may need to handle the same pressure level as stainless steel.
How to Choose a Flow Meter for the Test
 Consistent Flow – As long as there are no leaks or forks in the pipe, the flow rate should be consistent throughout. As a result, the flow meter should be installed in areas with a consistent flow stream.
 Flow velocity is inversely proportional to the pipe’s crosssectional area at any given flow rate. Smaller pipes result in faster flow rates, while larger pipes result in slower flow rates. As a result, we do not recommend using a small flow meter on a large pipe. It will be an energy waste, and the flow velocity will be too fast to measure the flow rate.
 Even for the same pipe size, the inner diameter will differ between the US and Japanese standard pipe. DN is defined as the outer diameter of a standard pipe. ID could be estimated as the inner diameter of a standard pipe.
 Make any metric or imperial conversions when calculating, if required. 1000ml = 1l; 1mm = 0.001m.
Summary
When you increase the size of your pipes and fittings, it can increase the water pressure and decreases the velocity, through water flow will be increased. This means that the amount of force that water can exert on a pipe or fitting is decreased. The larger the diameter and the lower the pressure, the more likely it is that water will flow through your pipes and fittings. If the water flow is high then the pressure will increase as well.
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