Fluid Dynamic Calculators

Fluid Flow Through the Nozzle

In this calculation, a fluid flow with a density ρ running through the nozzles or holes with a diameter D under the action of hydrostatic pressure P is considered. As a result of calculation, the flow velocity W is determined according to the Torricelli formula:

W = μ*(2P / ρ) ^1/2

μ - flow rate coefficient, depending on the nozzle type.

The flow rate Q is also calculated.

flow through nozzles

Calculation of the flow through the nozzles

INITIAL DATA

P - Hydraulic pressure;

ρ - Fluid density;

d - Hole or nozzle diameter.

RESULTS DATA

W - Average velocity of the flow;

Q - Volumetric flow rate through the nozzle.

Metric Imperial

Pressure (P)

Fluid density (ρ)

Diameter (d)

Hole

Nozzle with sharp inlet (I)

Nozzle with smooth inlet (II)

Cone nozzle (III)

Flow velocity (W)

Volumetric flow rate (Q)

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BASIC FORMULAS

Volumetric flow rate:

Q = μ*A*(2P/ρ)^0.5;

Flow velocity:

W = μ*(2P/ρ)^0.5;

A = πd² / 4 - Nozzle sectional area;

μ = 0.62 - flow rate coefficient for the hole;
μ = 0.83 - for nozzle with sharp inlet edge (figure I);
μ = 0.97 - for nozzle with smooth inlet edge (figure II);
μ = 1.15 - for cone nozzle with smooth inlet edge (figure III). Nozzle taper 7° < β < 12°.

INITIAL DATA

P - Hydraulic pressure;

ρ - Fluid density;

d - Hole or nozzle diameter.

RESULTS DATA

W - Average velocity of the flow;

Q - Volumetric flow rate through the nozzle.

FLUID PROPERTIES (at 20 °C)

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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