How to calculate pressure, velocity, and flow in pipeline design?

How to calculate pressure, velocity and flow in pipeline design?

In the actual industrial pipeline design, we required to design a reasonable engineering scheme that meets the actual production requirements according to the relevant technical documents given by the users. Therefore, how to determine the flow velocity V, pressure P, and flow rate Q in the pipeline. become more important.

The relationship between flow velocity V, pressure P, and flow rate Q

We take a example to expalin the relationship between these three factors.

Here a pipe size with φ25.4×1.65, measured medium is nitrogen gas, working pressure P=0.8MPa, working temperature t=20℃, then how to find the flow rate Q under working conditions?

First to calcualte the flow rate of the medium flowing through the pipeline in 1h, that is below:
Q=VπR2 x 3600

Q： volume flow — m³

V： medium velocity — m/s

R： pipe radius — m

we have below flow rate calculation formula:

In real applications, the flow velocity (V) in the pipeline is affected by many factors (like operating pressure, pipeline diameter, gas usage, etc.), so a reasonable flow velocity should be determined when design the pipeline.

Normaly for liquid measurement velocity is 0.5~3m/s, for gas flow rate is 10~30m/s.

Now assuming operating pressure is 0.8Mpa, we take:
Velocity V=10m/s ,
The inner diameter of the pipe is 22.1mm
Then the flow rate per hour under the working condition is:

How to convert to standard flow?

In actual production, the operating pressure of gas is often different from plant to plant, in case of trade friction, we need to find the common standard conditions for metering the flow rate under working conditions.

Here we bring the Ideal Gas Law to calculate the flow rate under a standard conditions.

The gas is affected by various factors in the actual use process, and its related parameters are often constantly changing, so the gas is often regarded as an ideal gas in the actual engineering calculation, so as to roughly calculate its actual flow rate.

The formula is : PV=nRT

P—gas absolute pressure KPa
V—gas volume m3
n—the amount of substance in the gas kmol
R—gas molar constant 8.314kj/(kmol .K)
T is the thermodynamic temperature K of the gas
t – working temperature ℃

So under working conditions and standard conditions there are:
P0V0=nRT0 (standard condition)
P1V1=nRT1 (working condition)
Combining the two formulas gives:
V0=(P1/P0)x(T0/T1)
= V1(P1/P0)x【273/(273+t)】

Note: where P1 is absolute pressure, P0 is standard atmospheric pressure

and convert the volume flow to standard flow formula is:

volume flow convert to standard flow formula

Standard condition and working condition flow conversion formula and example

The difference between standard condition and working condition

Working condition: flow rate in actual working state, unit: m³/h
Standard condition: flow rate at a temperature of 20°C and an atmospheric pressure (101.325kPa), unit: Nm³/h
Note: The standard conditions usually referred to are the temperature of 0°C (273.15 Kelvin) and the pressure of 101.325 kPa (1 standard atmospheric pressure, 760 mm Hg), which is different from the provisions of my country’s industrial gas standard conditions.
The units in both states are the same, but the corresponding flows are different. In addition, different countries refer to different states.

Calculation equation

According to the ideal gas equation of state: pV=nRT.
This equation has 4 variables: p is the pressure of the ideal gas, V is the volume of the ideal gas, n is the amount of gas substance, and T is the thermodynamic temperature of the ideal gas; there is also a constant: R is the ideal gas constant.
PV/T=nR is a constant, so P1×V1/T1=P2×V2/T2
Under the standard condition, the volume flow is V0, the temperature T0=273+20=293k, the pressure P0=101.325Kpa=0.101325Mpa,
Under the working conditions, the volume flow is V, the temperature is T (degree Celsius), the pressure is P (gauge pressure, Mpa), and the change of ignoring the compression factor is V*(P+0.101325)/(T+273)=V0*P0/T0

Conversion example between standard condition and working condition

Usually, the flow we say is the flow in the standard state for the convenience of a unified unit; and the actual flow recorded by the factory operation is basically the flow under the working condition.
1. Example of conversion from standard condition flow to working condition flow:
Question: The rated gas output of the air compressor is 2 cubic meters per minute, and the pipeline pressure is 8 kg. What is the actual flow rate of the pipeline?
Answer: For a rough calculation, assume that the compressed air temperature is 20 degrees.
Working condition flow=2/(0.8+0.101325)*0.101325=0.2248 cubic/min
In the formula: 0.101325 is the absolute pressure of the atmosphere; 0.8 is the pipeline pressure, the unit is MPa.
2. Example of conversion from working condition flow to standard condition flow:
Question: The pressure of the oxygen pipeline is 12 kg, and the flow rate under working conditions is 10 cubic meters per hour. What is the flow rate under standard conditions?
Answer: Assuming the temperature is 20 degrees, do not participate in the calculation.
Standard flow rate=10/0.101325*(1.2+0.101325)=128.43 cubic meters/hour
In the formula: 0.101325 is the absolute pressure of the atmosphere; 1.2 is the pipeline pressure, the unit is MPa.

How to select a right flow meter for measurement?

Example: The actual working pressure of a gas supply pipeline is 0.8MPa~1.2MPa(gauge pressure), the medium temperature range is -5℃~40℃, and the gas supply volume is 3000~10000Nm³/h (standard flow rate), Without considering the composition of natural gas, it is required to determine the specification and model of the flowmeter.
According to the gas equation, first we need to convert the standard flow into the working flow, and then select the appropriate diameter. The gas equation is as follows:
Qb=Q×PTb/PbT×Zb/Zg=QCF2
In the formula: C is the conversion factor; F is the gas compression factor
calculate:
①When the medium pressure is the lowest and the temperature is the highest, it should have the maximum standard volume flow rate,
That is, Qb=Q×PTb/PbT×Zb/Zg=QCF2=1200.87m³/h
② When the medium pressure is the highest and the temperature is the lowest, it should have the minimum standard volume flow rate,
That is, Qmin=213.51m³/h
From the above calculation results, it can be known that the flow range of the flowmeter to be selected is (214-1200) m³/h.
According to the calculated flow range, select a flowmeter that meets the requirements of the working conditions.