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Orifice Flow Calculator

Calculate flow through orifices, nozzles, and constrictions using discharge coefficients

Parameters

mⓘ
Paⓘ
ⓘ
kg/m³ⓘ
Show Trail

Controls

xⓘ

Calculated Values

Flow Rate:
0.00;m3/s0.00;m³/s
Velocity:
0.45;m/s0.45;m/s
Power:
0.01;W0.01;W
Reynolds Number:
8944.27;8944.27;

Examples

Example 1: Water Flow Through Orifice

Water flowing through a sharp-edged orifice.

  • Flow Rate: 0.000.00
  • Velocity: 14.1414.14
  • Power: 0.050.05
  • Reynolds Number: 282.80282.80

Example 2: Air Flow Through Nozzle

Air flowing through a rounded nozzle.

  • Flow Rate: 0.000.00
  • Velocity: 28.5728.57
  • Power: 0.370.37
  • Reynolds Number: 350.00350.00

Example 3: Oil Flow Through Valve

Oil flowing through a control valve.

  • Flow Rate: 0.010.01
  • Velocity: 48.5048.50
  • Power: 5.105.10
  • Reynolds Number: 2061.002061.00

Visualization

Orifice Flow

Orifice flow occurs when a fluid passes through a constriction or opening in a pipe or tank. The flow rate through an orifice depends on the pressure difference, orifice size, and discharge coefficient. This principle is widely used in flow measurement and control applications.

The basic orifice flow equation is: Q = C_d A √(2ΔP/ρ), where Q is flow rate, C_d is discharge coefficient, A is orifice area, ΔP is pressure difference, and ρ is fluid density. The discharge coefficient accounts for energy losses and flow contraction.

The discharge coefficient (C_d) typically ranges from 0.6 to 0.9 and depends on the orifice geometry, Reynolds number, and edge conditions. Sharp-edged orifices have C_d ≈ 0.61, while rounded orifices can have higher values.

When fluid flows through an orifice, it contracts to a smaller area (vena contracta) downstream of the orifice. The contraction coefficient (C_c) is the ratio of the contracted area to the orifice area, typically about 0.62 for sharp-edged orifices.

Orifice flow is used in flow meters, control valves, nozzles, and many industrial applications. The principle is also applied in carburetors, fuel injectors, and hydraulic systems.

Key Concepts

  • Flow Rate: Q = C_d A √(2ΔP/ρ)
  • Discharge Coefficient: C_d (accounts for losses)
  • Contraction Coefficient: C_c (area ratio)
  • Velocity Coefficient: C_v (velocity ratio)
  • Vena Contracta: Minimum flow area
  • Pressure Recovery: Downstream pressure increase

Real-World Applications

  • Flow Meters: Orifice plate meters
  • Control Valves: Flow regulation
  • Nozzles: Jet propulsion and spraying
  • Carburetors: Fuel-air mixing
  • Hydraulic Systems: Flow control

Explore Further

More fluid mechanics tools

Physics Equations

Flow Rate:
Q=CdA2ΔPρQ = C_d A \sqrt{\frac{2\Delta P}{\rho}}
Orifice Area:
A=πd24A = \frac{\pi d^2}{4}
Velocity:
v=2ΔPρv = \sqrt{\frac{2\Delta P}{\rho}}
Reynolds Number:
Re=ρvdμRe = \frac{\rho v d}{\mu}
Power:
P=QΔPP = Q \Delta P

Step-by-Step Solution

See how the main results are calculated.

1

Step 1: Identify Parameters

First, we identify the parameters needed for orifice flow calculation:

Equation:

Q=CdA2ΔPρQ = C_d A \sqrt{\frac{2\Delta P}{\rho}}

Calculation:

d=0.02 m,ΔP=100 Pa,Cd=0.61,ρ=1000 kg/m3d = 0.02 \text{ m}, \Delta P = 100 \text{ Pa}, C_d = 0.61, \rho = 1000 \text{ kg/m}^3

Explanation:

These are the orifice diameter, pressure difference, discharge coefficient, and fluid density.

2

Step 2: Calculate Orifice Area

Calculate the cross-sectional area of the orifice:

Equation:

A=πd24A = \frac{\pi d^2}{4}

Calculation:

A=π(0.02)24=0.000314 m2A = \frac{\pi(0.02)^2}{4} = 0.000314 \text{ m}^2

Explanation:

The area of a circular orifice is πd²/4.

3

Step 3: Calculate Velocity

Calculate the theoretical velocity through the orifice:

Equation:

v=2ΔPρv = \sqrt{\frac{2\Delta P}{\rho}}

Calculation:

v=2(100)1000=0.45 m/sv = \sqrt{\frac{2(100)}{1000}} = 0.45 \text{ m/s}

Explanation:

This is the velocity based on the pressure difference and fluid density.

4

Step 4: Calculate Flow Rate

Apply the discharge coefficient to get actual flow rate:

Equation:

Q=CdAvQ = C_d A v

Calculation:

Q=0.61×0.000314×0.45=0.000086 m3/sQ = 0.61 \times 0.000314 \times 0.45 = 0.000086 \text{ m}^3/\text{s}

Explanation:

The discharge coefficient accounts for energy losses and flow contraction.

5

Step 5: Calculate Power

Calculate the power associated with the flow:

Equation:

P=QΔPP = Q \Delta P

Calculation:

P=0.000086×100=0.009 WP = 0.000086 \times 100 = 0.009 \text{ W}

Explanation:

This represents the power required to maintain the pressure difference.

Frequently Asked Questions (FAQ)

What is orifice flow?

Orifice flow occurs when a fluid passes through a constriction or opening. The flow rate depends on pressure difference, orifice size, and discharge coefficient.

What is the discharge coefficient?

The discharge coefficient (C_d) accounts for energy losses and flow contraction. It typically ranges from 0.6 to 0.9, with sharp-edged orifices having C_d ≈ 0.61.

What is the vena contracta?

The vena contracta is the point of minimum flow area downstream of an orifice, where the fluid stream contracts to its smallest cross-section.

How does pressure affect orifice flow?

Flow rate is proportional to the square root of pressure difference. Doubling the pressure difference increases flow rate by √2 ≈ 1.41 times.

What are the applications of orifice flow?

Orifice flow is used in flow meters, control valves, nozzles, carburetors, fuel injectors, and hydraulic systems for flow measurement and control.

Practice MCQs

  1. The orifice flow equation is:
  2. The discharge coefficient for sharp-edged orifices is approximately:
  3. Flow rate through an orifice is proportional to:
  4. The vena contracta is:
  5. As orifice diameter increases, flow rate:

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