# Orifice Flow Rate

on . Posted in Flow Instrument

Orifice flow rate, abbreviated as Q, also called discharge coefficient equation, is the rate at which fluid flows through an orifice, which is a small opening or hole in a pipe or vessel.  When a fluid, such as a liquid or gas, passes through an orifice, it experiences a pressure drop due to the restriction created by the smaller area cross-section of the orifice compared to the pipe or vessel.  The flow rate through an orifice can be determined using various equations, including the Bernoulli's equation, the continuity equation, and empirical formulas derived from experimental data.

The discharge coefficient takes into account the shape of the orifice, the Reynolds number, and other factors that influence the flow behavior.  It is typically determined experimentally or obtained from published tables or correlations.  It's important to note that the orifice equation assumes that the flow is incompressible, steady, and adiabatic (without heat transfer).  In reality, the flow may be affected by factors such as viscosity, compressibility, and turbulence, which may require further corrections or considerations in specific applications.

Overall, the orifice flow rate is a key parameter used in fluid dynamics and is commonly used in industries such as oil and gas, chemical processing, and HVAC systems to measure and control fluid flows.

## Orifice Flow Rate formula

$$\large{ Q = A_o \; C_d \; \sqrt { 2 \; G \; h } }$$     (Orifice Flow Rate)

$$\large{ A_0 = \frac{ Q }{ C_d \; \sqrt{ 2 \; G \; h } } }$$

$$\large{ C_d = \frac{ Q }{ A_o \; \sqrt{ 2 \; G \; h } } }$$

$$\large{ G = \frac{ \left( \frac{ Q }{ C_d \; A_o } \right)^2 }{ 2 \; h } }$$

$$\large{ h = \frac{ \left( \frac{ Q }{ A_o \; C_d } \right)^2 }{ 2 \; G } }$$

### Solve for Q

 orifice area, Ao orifice discharge coefficient, Cd orifice gravitational constant, G orifice center of head, h

### Solve for Ao

 orifice flow rate, Q orifice discharge coefficient, Cd orifice gravitational constant, G orifice center of head, h

### Solve for Cd

 orifice flow rate, Q orifice area, Ao orifice gravitational constant, G orifice center of head,h

### Solve for G

 orifice flow rate, Q orifice area, Ao orifice discharge coefficient, Cd orifice center of head, h

### Solve for h

 orifice flow rate, Q orifice area, Ao orifice discharge coefficient, Cd orifice gravitational constant, G

Symbol English Metric
$$\large{ Q }$$ = orifice flow rate $$\large{\frac{ft^3}{sec}}$$ $$\large{\frac{m^3}{s}}$$
$$\large{ A_o }$$ = orifice area $$\large{ in^2 }$$ $$\large{ mm^2 }$$
$$\large{ C_d }$$ = orifice discharge coefficient $$\large{ dimensionless }$$
$$\large{ G }$$ = orifice gravitational constant $$\large{\frac{lbf-ft^2}{lbm^2}}$$ $$\large{\frac{N -m^2}{kg^2}}$$
$$\large{ h }$$ = orifice center of head $$\large{ in }$$ $$\large{ mm }$$