# Orifice Flow Calculator

Created by Gabriela Diaz
Last updated: Aug 01, 2022

Use the orifice flow calculator to calculate the flow through an orifice. Orifices and orifices plates are common implements in fluid mechanics and hydraulics that are often used for flow metering or flow restriction.

• What is orifice flow?;

• How to derive the orifice equation; and

• What happens with the fluid's velocity and pressure at the restriction.

## What is orifice flow rate? — Flow through an orifice equation

Similar to a venturi tube and nozzle meters, an orifice plate is another type of flow meter device based on the pressure differences across it. The orifice meter consists of a circular metal plate with a concentric hole (a disk) through which the flow travels. This device is also used to control and restrict flow rate, as well as to reduce pressure. In these cases is known as a restriction plate.

In one of its typical configurations, the orifice plate is installed inside the pipe and attached to pipe ends with flanges, introducing a sudden diameter change. Let's suppose we followed the fluid traveling through this section of the pipe. We'll see that initially, it moves through a larger pipe diameter, encounters the diameter decrement, and finally goes back to the original pipe size.

This reduction in diameter, which implies a decreased cross-sectional area, translates into a rise in the fluid's velocity at the orifice and all the way through the vena contracta region, after which velocity reduces. We may see this more clearly if we recall mass conservation in the form of the continuity equation:

\small \begin{aligned} \dot{m_1} &= \dot{m_2} \\ \rho \ A_1 \ V_1 &= \rho \ A_2 \ V_2 \\ V_2 &= \cfrac{A_1 \ V_1}{A_2} \end{aligned}

where:

• $\dot{m_1}$, $A_1$ and $V_1$ — Mass flow, cross-sectional area and velocity of the fluid before the obstruction;
• $\dot{m_2}$, $A_2$ and $V_2$ — Mass flow, cross-sectional area and velocity of the fluid after the obstruction; and
• $\rho$ — Density of the fluid.

We have a dedicated flow rate calculator, where you can learn the difference between volumetric and mass flow rates!

If we apply Bernoulli's equation at these same two points, we'll see that an increase in the velocity of the fluid, which implies a rise in its kinetic energy, means that another form of energy has to reduce. Assuming that there's no significant change in the elevation, we can omit the hydrostatic pressure terms ($\rho \ g \ h$), and the energy conservation is expressed as:

$\small P_1 + \cfrac{\rho \ V_1^2}{2} = P_2 + \cfrac{\rho \ V_2^2}{2}$

Where $P_1$ and $P_2$ are the static pressures at the corresponding points.

This expression mathematically supports the pressure drop effect. It makes it easier to see that in order for the kinetic energy at point 2 to rise ($\rho V_2^2/2$), the pressure energy at that point must decrease ($P_2$).

We can rewrite the above for the particular case of a free discharge setup, such as an atmospheric tank with an opening, operating in a steady flow and with constant head $H$:

$\small \cfrac{P_1}{\rho \ g} + \cfrac{V_1^2}{2 \ g} = P_2 + \cfrac{V_2^2}{2 \ g}$

The head of liquid $H$ can be expressed as: $P_1 /\rho \ g = H$, and because this is a free discharge case, the pressure at point 2 equals the atmospheric, thus: $P_2 /\rho \ g = 0$. Furthermore, because the velocity inside the tank is relatively small compared to the velocity at which the fluid leaves the tank, $V_1 = 0$. Substituting these in the equation above:

$\small H + 0 = 0 + \cfrac{V_2^2}{2 \ g}$

To find the velocity at point 2:

$\small V_2 = \sqrt{2 \ g \ H}$

Orifice flow refers to the flow rate through an orifice. To get this flow rate, we multiply the above by the orifice's cross-sectional area and by the discharge coefficient $C_d$. This last is included to account for the hydraulic losses of the system:

$\small Q = C_d \ A \ \sqrt{2 \ g \ H}$

where:

• $Q$ — Volumetric flow rate or discharge;
• $C_d$ — Discharge coefficient, this one is dimensionless;
• $A$ — Cross-sectional area of the orifice;
• $g$ — Acceleration of gravity; and
• $H$ — Head of liquid above the center of the orifice.

This is the equation that the orifice flow calculator uses to calculate the flow through an orifice.

## Using the orifice flow calculator

By simply entering the values of some variables, this orifice flow calculator can instantly help you determine the flow rate through an orifice plate. Let us go through how to utilize this tool step by step:

1. Begin by indicating the Diameter of orifice (d).

2. In the field below, Area of orifice (A), the calculator will show you the area of the orifice.

3. Proceed to enter the Coefficient of discharge (Cd).

4. Next, enter the mean center line in the Center line head (H) row.

5. With these numbers, the orifice flow calculator will display the corresponding flow rate in the Discharge (Q) field.

💡 This calculator uses the gravitational acceleration of 9.81 m/s². If you'd like to adjust this value, you may do so by using the Advanced mode of this tool.

Gabriela Diaz Diameter of orifice (d)
in
Area of orifice (A)
in²
Coefficient of discharge (Cd)
in
Discharge (Q)
ft³/s
People also viewed…

### Mach number

With our Mach number calculator you will need only your speed to know if you are going supersonic or not! 