# Discharge Coefficient

on . Posted in Fluid Dynamics

Discharge coefficient, abbreviated as $$C_d$$, also called coefficient of discharge, a dimensionless number, is the ratio of actual discharge to the theoretical discharge.  It is used to characterize the performance of various fluid flow devices, such as nozzles, orifices, and venturis, by quantifying the amount of fluid flow that is lost due to friction and other effects.  It relates the actual flow rate of the fluid to the theoretical flow rate based on ideal conditions.

The discharge coefficient is dependent on various factors, including the shape and dimensions of the flow passage, the Reynolds number, and the properties of the fluid being considered.  It is important to note that the discharge coefficient is often determined experimentally through calibration or testing of the specific flow measurement device.  Different flow devices have different discharge coefficient values, and they can vary depending on the operating conditions.  By incorporating the discharge coefficient into flow calculations, more accurate flow rate measurements can be obtained for a given flow device and fluid system.

## Discharge Coefficient formula

$$\large{ C_d = \frac{ \dot m_f }{ \rho \; Q } }$$

### Discharge Coefficient - Solve for Cd

$$\large{ C_d = \frac{ \dot m_f }{ \rho \; Q } }$$

 mass flow rate, mf density, ρ volumetric flow rate, Q

### Discharge Coefficient - Solve for mf

$$\large{ \dot m_f = C_d \; \rho \; Q }$$

 discharge coefficient, Cd density, ρ volumetric flow rate, Q

### Discharge Coefficient - Solve for ρ

$$\large{ \rho = \frac{ \dot m_f }{ C_d \; Q } }$$

 mass flow rate, mf discharge coefficient, Cd volumetric flow rate, Q

### Discharge Coefficient - Solve for Q

$$\large{ Q = \frac{ \dot m_f }{ C_d \; \rho } }$$

 mass flow rate, mf discharge coefficient, Cd density, ρ

Symbol English Metric
$$\large{ C_d }$$ = discharge coefficient $$\large{ dimensionless }$$
$$\large{ \dot m_f }$$ = mass flow rate $$\large{\frac{lbm}{sec}}$$ $$\large{\frac{kg}{s}}$$
$$\large{ \rho }$$  (Greek symbol rho) = density of fluid $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$
$$\large{ Q }$$ = volumetric flow rate $$\large{\frac{ft^3}{sec}}$$ $$\large{\frac{m^3}{s}}$$ 