Fluid Flow Velocity Profile in Pipe | Online Calculator

Fluid Dynamic Calculators

Fluid Flow Velocity Profile in Pipe

When the fluid flows in the pipeline, a boundary layer is formed near the pipe wall. A homogeneous flow entering the pipe has the same velocity profile over the cross-section. Then the flow deceleration near the surface, boundary layer formation and velocity profile distortion occur. At that, the flow can be divided into zones: an inlet zone, in which a core with an undisturbed flow exists along with the increasing boundary layer, a stabilization zone, and a stabilized motion zone, where both turbulent and laminar flows, determined by the Reynolds number may exist.

In this calculation, a fluid flow with density ρ, dynamic viscosity μ, which moves with a flow rate Q through a pipe of diameter D is considered. As a result of calculation, the flow velocity Wy is determined at any distance Y from the pipe wall. The Reynolds number Re, thickness of the laminar layer Ul, transitional turbulent layer Ut and average flow velocity W are also calculated. The most accurate results are achieved at Re > 105.

Hydrodynamic of Pipelines
Hydrodynamic of Pipes

INITIAL DATA

Q - Volumetric flow rate;

ρ - Fluid density;

μ - Dynamic fluid viscosity (see table below);

D - Pipe inner diameter;

Y - Distance from internal pipe surface to calculated point.

RESULTS DATA

W - Average velocity of the flow;

Wy - Fluid velocity at calculated point;

Ul - Laminar sublayer thickness;

Ut - Turbulent sublayer thickness;

Re - Reynolds number.

Volumetric flow rate (Q)

Liquid density (ρ)

Dynamic viscosity (μ)

Pipe diameter (D)

Distance (Y)

Average velocity (W)

Velocity at point Y (Wy)

Sublayer thickness (Ul)

Sublayer thickness (Ut)

Reynolds number (Re)

BASIC FORMULAS

Reynolds number:

Re = W*D*ρ / μ

Laminar sublayer thickness:

Ul = 68.4*Re-0.875*D / 2;

Average velocity:

W = 4Q / π*D2;

Wall friction stress:

τ = 0.079*Re-0.25*ρ*W2 / 2;

Fluid velocity at pipe axis:

τ / 0.5ρWaxis = 0.37 / [Lg(5Re*Waxis)]2.584;

Fluid velocity at point Y:

Wy / Waxis = (2Y / D)n;

n = 2.7(τ / ρ*Waxis2)0.5 / [1 - 2.7(τ / ρ*Waxis2)0.5].

INITIAL DATA

Q - Volumetric flow rate;

ρ - Fluid density;

μ - Dynamic fluid viscosity (see table below);

D - Pipe inner diameter;

Y - Distance from internal pipe surface to calculated point.

RESULTS DATA

W - Average velocity of the flow;

Wy - Fluid velocity at calculated point;

Ul - Laminar sublayer thickness;

Ut - Turbulent sublayer thickness.

Re - Reynolds number.

FLUID PROPERTIES

Fluid

Dynamic viscosity

Pa*s

(lb*s/ft2)

Density

Kg/m3

(lb/ft3)

Water

0.001

(0.0000208)

1005

(62.8)

Freon-11

0.00048

(0.00001)

1494

(93.4)

Freon-12

0.00028

(0.00000586)

1330

(83.1)

Freon-22

0.00025

(0.00000522)

1202

(75.1)

Freon-113

0.00074

(0.0000155)

1573

(98.3)

Kerosene

0.00256

(0.0000535)

804

(50.25)

Benzene

0.00069

(0.0000144)

879

(54.9)

Glycerol

1.393

(0.029)

1261

(78.8)

Ethanol

0.00122

(0.0000255)

789

(49.3)

Mercury

0.00159

(0.0000332)

13545

(846)

Linseed oil

0.044

(0.000919)

924

(57.75)

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