Hydraulic calculation of pipelines

The hydrodynamic calculation of the flow of an incompressible fluid reduces to solving the Bernoulli equation for two consecutive sections:

ρgh₁ + P₁ + α₁×w₁²ρ / 2 = ρgh₂ + P₂ + α₂×w₂²ρ / 2 + ΔP_пот., where:

h₁, h₂ – the height of the starting and ending points of the pipeline;
w₁, w₂ – flow rates at the start and end points of the pipeline;
P₁, P₂ – hydrostatic pressures;
α₁, α₂ – Coriolis coefficients taking into account the uneven distribution of velocities over the cross section;
ΔP_пот. – loss of pressure to overcome resistance.

The hydraulic online calculation, presented in this section allows you to calculate the flow characteristics of an incompressible fluid, as well as the flow of a compressible fluid or high pressure gas. Both calculations are performed for a straight pipe.

When solving such problems by the finite element method in the ANSYS software, it is extremely important that the mesh size in the wall layer of the pipeline does not exceed certain values ​​in the radial direction. The algorithms in this section calculate the minimum size of the first cell, recommended by the developers with the value of the wall function Y ⁺ = 30. In general, the value of the wall function should be within 30 < Y⁺ < 300.

Hydrodynamic calculation of an incompressible fluid pipeline

When conducting a hydrodynamic calculation, the Reynolds number is determined:

Re = W×D×ρ / μ;, where

μ – dynamic fluid viscosity;
W – flow rate;
D – pipe diameter.

The thickness of the laminar sublayer is determined along the inner surface of the pipe:

δ = 68,4×Re^-0.875×D / 2

The friction coefficient Δ is determined depending on the roughness of the inner surface of the pipe:

λ = 0,316×Re ^-0.25 at δ > Δ
λ = 0,11(Δ / D + 68 / Re) ^0.25 at δ < Δ

The D’Arcy formula determines pressure loss in straight sections:

ΔP = λ×(L / D)×(W²ρ / 2)

Pressure loss on local resistances:

ΔP = ΣK_i×(W²ρ / 2)

Summarizing the results obtained, we obtain a total pressure loss in a certain section of the pipeline.

Initial data:

Q – fluid flow rate in the pipeline, liters per second;

ρ – fluid density, kilogram / meter ³;

μ – dynamic fluid viscosity, pascal×second;

ΔH – elevation difference of the starting and ending points of the pipeline section, meters;

D – the inner diameter of the pipeline, millimeters;

L – pipeline length, meters;

ΣK_i – total local resistance coefficient;

Δ – absolute roughnessof the inner wall of the pipe, millimeters.

Ref 12

Calculation of a high pressure gas pipeline

When high pressure gases are transported in pipelines, due to pressure losses to overcome resistance, the specific volume of gas increases and its density decreases. Moreover, the change in pressure at the elementary length dL is:

dP = – λ×(1/D)×(W² / 2)×ρdL, wherein:

W = W₀(TP₀ / T₀P);

ρ = ρ₀(T₀P/ TP₀);

ρ₀, W₀ – gas density and gas flow rate under normal physical conditions(NPC);
T₀ = 273°C;
P₀ = 101300 Pa.

Substituting the resulting expressions:

pdP = – λ×(W₀²ρ₀ / 2D)×(T / T₀)×P₀dL;

After integration:

(P_fin² – P_start²) / 2 = -λ(L / D)(W₀²ρ₀ / 2)(P₀T / T₀);

It’s easy to get pressure loss from here:

ΔP = P_start(1 – (1 – λ(L / D)×(W₀²ρ₀)×(P₀T / P_start²T₀)) ^1/2);

P_start – absolute pressure at the starting point of the pipeline section.

The friction coefficient is the same as in the calculation of the flow of an incompressible fluid.

Initial data:

Q – gas flow in the pipeline under normal physical conditions, in cubic meters per hour;

ρ – gas density under normal physical conditions, in kilogram / meter ³;

T – gas temperature, in °C;

μ – dynamic viscosity of gas at operating temperature, in pascals×sec;

D – the inner diameter of the pipeline, in millimeters;

L – pipeline length, in meters;

ΣK_i – total local resistance coefficient;

Δ – absolute roughness of the inner wall of the pipe, in millimeters.

P_н – overpressure at the inlet of the pipeline, in pascals;

Ref 12

Other calculators

– pipeline strength calculation

– thin-walled axisymmetric shell

– thick-walled pipe under internal and external pressure

– composite pipe calculation

– free convection for a horizontal surface

– free convection for a vertical surface

– heat transfer coefficient of a flat wall

– heat transfer coefficient of the inner wall of the pipe

– heat transfer coefficient of the outer wall of the pipe

– heat transfer coefficient of the outer wall of the group of pipes

– heat transfer coefficient through a flat wall

– heat transfer coefficient through a cylindrical wall