# Coefficient of Discharge Calculator

The coefficient of discharge calculator will help you determine the **ratio between the theoretical and actual discharge** or flow rate values for a fluid flow. Whether it is water supply to your house, gas pipelines, or water in an artificial canal, the estimated or **theoretical fluid flow** used to design these systems is **always higher than the actual flow rate** for fluids.

The difference is in a hydraulic system's **irrecoverable losses**. Therefore, a parameter, discharge coefficient, is introduced into the calculations to account for the reduction in the flow rate. It is a function of **area, flow rate, and head or pressure drop**. So what is it all about? Read on to understand how to calculate the coefficient of discharge.

## What is discharge coefficient?

In simple terms, the discharge coefficient is the ratio of **theoretical and actual flow** rates. The coefficient of discharge is a dimensionless parameter. It is one of the three hydraulic coefficients, which are:

- Coefficient of discharge, $C_d$;
- Coefficient of contraction, $C_c$; and
- Coefficient of velocity, $C_v$.

While the coefficient of discharge deals with the **flow rate**, the **coefficient of contraction** is associated with the **change in the area of the cross-section** and area of the jet. Lastly, the **coefficient of velocity relates to a fluid jet's actual and theoretical velocities**. The three hydraulic coefficients are related to each other using the equation below.

## Discharge coefficient — Orifice, venturi, weir, open channel flows and others

Consider a **fluid flow with a constant cross-sectional area**. The coefficient of discharge, $C_d$ is:

where:

- $Q_{act}$ – Actual discharge; and
- $Q_{th}$ – Theoretical discharge.

The actual discharge can be measured at one end of the orifice and denoted as $\dot{m}$ or $Q_{act}$ whereas the **theoretical discharge is given by the equation**:

where:

- $\rho$ – Density of fluid;
- $A$ – Area of cross section;
- $c$ – Flow velocity;
- $\Delta P$ – Change in pressure;
- $g$ – Acceleration due to gravity; and
- $H$ – Head of fluid i.e., the
**height or elevation of top surface of liquid**.

Therefore, the coefficient of discharge becomes:

In most cases, the discharge coefficient value is between `0.6-0.65`

. The discharge coefficient is also related to the flow resistance, which is the **resistance offered by the surroundings** in which the fluid flow occurs. The **flow resistance**, $k$, is related to the coefficient of discharge as:

## How to calculate coefficient of discharge

To calculate discharge coefficient:

- Select the
`mode`

based on the parameters available to you. You can either calculate this discharge coefficient parameter using the hydraulic head or the change in pressure. - If the cross-section is circular, you can enter the pipe diameter, $d$.
- Enter the
**area of cross-section**, $A$. - Insert the fluid
**head**, $H$. - Fill in the
**actual discharge**, $Q_{act}$. - The calculator will return the
**coefficient of discharge**and**flow resistance**.

**Gravitational accleration**

If you wish to adjust the value of acceleration due to gravity, you can enable this calculator's `advanced mode`

.

## Example: Using the coefficient of discharge calculator

Find the actual discharge for a fluid flow through an orifice having a diameter of `40 mm`

and head `10 m`

. Take the coefficient of discharge for the orifice meter as `0.6`

.

- Select the
`mode`

using**hydraulic head**. - Fill in the
**diameter**, $d = 40 \text{ mm}$. - The calculator will return the
**area of cross-section**, $A = 0.00125664 \text{ m}^2$. - Insert the fluid
**head**, $H = 10 \text{ m}$. - Fill in the
**discharge coefficient**, $C_{d} = 0.6$. - The
**actual discharge**, $Q_{act}$ is:

- The
**flow resistance**, $k$ is:

Now let's try **another example**. Use the calculator to find the `change in pressure`

for a fluid flow through a `50 mm`

orifice at a mass flow rate of `20 kg/s`

. Take the coefficient of discharge as `0.909`

.

To estimate the change in pressure:

- Select the
`mode`

using**change in pressure**. - Fill in the
**diameter**, $d = 50 \text{ mm}$. - The calculator will return the
**area of cross-section**, $A =1963.5 \text{ mm}^2$. - Enter the
**mass flow rate**, $\dot{m} = 20 \text{ kg/s}$. - Fill in the
**discharge coefficient**, $C_{d} = 0.909$. - The
**change in pressure**, $\Delta P$ is:

## FAQ

### What do you mean by discharge coefficient?

The discharge coefficient is the **ratio of actual discharge to the theoretical discharge** for a fluid flow. It is used to estimate the **losses for a system** and is among the three hydraulic coefficients, along with velocity coefficient and contraction coefficient.

### How do I calculate theoretical discharge?

To calculate theoretical discharge using head:

**Multiply**the**hydraulic head**with**acceleration due to gravity**.**Multiply**the resultant by`2`

.- Find the
**square root**of the product. **Multiply**the resulting value by the**area of cross-section**to obtain the theoretical discharge for a fluid flow.

### How do I calculate actual discharge?

To calculate actual discharge:

You'll need — stopwatch, a bucket with its capacity known.

**Start**the fluid flow.**Begin the timer**as the bucket starts to fill.**Stop the timer**when the bucket is filled.**Divide**the**bucket's capacity**with the**time duration**to find the actual discharge.

### How do I calculate discharge coefficient for an orifice flow?

To calculate discharge coefficient:

**Multiply**the**hydraulic head**by the**acceleration due to gravity**.**Multiply**the resultant by`2`

.- Find the
**square root**of the product. **Multiply**the resulting value by the**area of cross-section**to obtain the theoretical discharge for a fluid flow.**Divide**the**actual discharge**by the**theoretical discharge**to obtain discharge coefficient.