Orifice Head Loss
Orifice head loss, also called orifice pressure drop, is the pressure drop or decrease in fluid pressure caused by the presence of an orifice plate in a pipeline. It occurs due to the reduction in the flow area of the pipeline caused by the orifice plate, which results in increased fluid velocity and turbulence. The amount of head loss depends on several factors such as the size and shape of the orifice plate, the Reynolds number of the fluid flow, and the viscosity of the fluid. An orifice is a small, typically circular opening or hole in a pipe or vessel through which a fluid (liquid or gas) is allowed to pass. Orifices are commonly used in various engineering and industrial applications for purposes such as flow control, measurement, and restriction.
When fluid flows through an orifice, several factors contribute to the loss of pressure
 Constriction  The fluid is forced to pass through a smaller area at the orifice compared to the larger pipe or vessel it was flowing through. This constriction causes the fluid to accelerate, leading to a decrease in pressure according to Bernoulli's principle.
 Friction  The fluid experiences friction as it passes through the orifice, which further contributes to the pressure drop.
 Vortex Formation  In some cases, vortices or swirling currents may form downstream of the orifice, causing additional pressure losses.
The magnitude of the pressure drop or head loss depends on various factors, including the size and shape of the orifice, the properties of the fluid (density and viscosity), and the flow rate of the fluid. Engineers use mathematical equations and empirical data to calculate orifice head loss, which is important for designing systems where maintaining a specific pressure or flow rate is critical. Orifices are commonly used in applications such as flow meters, control valves, and pressurereducing devices. Understanding and accurately calculating orifice head loss is essential for optimizing the performance of these systems and ensuring that they operate within specified parameters.
Horizontal Orifice and Nozzle Head Loss formula 

\(\large{ \Delta h = \left( \frac{1}{2\;g} \right) \; \left( 1  \beta^4 \right) \; \left( \frac{ Q }{ C_d \; A_o \; Y } \right)^2 }\) (Horizontal Orifice and Nozzle Head Loss) \(\large{ g = \left( \frac{1}{2\;\Delta h} \right) \; \left( 1  \beta^4 \right) \; \left( \frac{ Q }{ C_d \; A_o \; Y } \right)^2 }\) \(\large{ \beta= \sqrt[4]{ 1 \;\; 2 \; g \; \Delta h \; \sqrt{ \frac{ Q }{ C_d \; A_o \; Y }} }}\) \(\large{ Q = \Delta h \; \frac{ 2 \; g }{ 1 \;−\; b^4 } \; \left( Cd \; Ao \; Y \right)^2 }\) \(\large{ Cd = \frac{1 }{ Ao \; Y } \; \frac{ 1 }{ \sqrt{ \frac{2 \; g }{1 \;−\; b^4 \; Q} } } }\) \(\large{ Ao = \frac{ \sqrt{ \frac{ 1 \;−\; b^4 \; Q }{ \Delta h \; 2 \; g} } }{ Cd \; Y} }\) \(\large{ Y = \frac{ \sqrt{ \frac{ 1 \;−\; b^4 \; Q }{ \Delta h} } }{ Cd \; Ao} }\) 

Solve for Δh
Solve for g
Solve for β
Solve for Q
Solve for Cd
Solve for Ao
Solve for Y


Symbol  English  Metric 
\(\large{ \Delta h }\) = head loss  \(\large{ ft }\)  \(\large{ m }\) 
\(\large{ g }\) = gravitational acceleration  \(\large{\frac{ft}{sec^2}}\)  \(\large{\frac{m}{s^2}}\) 
\(\large{ \beta }\) (Greek symbol beta) = ratio of pipe inside diameter to orifice diameter  \(\large{ dimensionless }\)  
\(\large{ Q }\) = orifice flow rate  \(\large{\frac{ft^3}{sec}}\)  \(\large{\frac{m^3}{s}}\) 
\(\large{ C_d }\) = orifice discharge coefficient  \(\large{ dimensionless }\)  
\(\large{ A_o }\) = orifice area  \(\large{ in^2 }\)  \(\large{ mm^2 }\) 
\(\large{ Y }\) = expansion coefficient (Y = 1 for incompressible flow)  \(\large{ dimensionless }\)  
Solve for: 

\(\large{ Y = \frac{ C_{d,c} }{ C_{d,i} } }\) \(\large{ C_{d,c} }\) = discharge coefficient compressible fluid \(\large{ C_{d,i} }\) = discharge coefficient incompressible fluid \(\large{ \beta }\) (Greek symbol beta) = \(\frac{d_0}{d_u}\) \(\large{ d_o }\) = orifice or nozzle diameter \(\large{ d_u }\) = upstream pipe inside diameter from orifice or nozzle 
Vertical Orifice and Nozzle Head Loss formula 

\(\large{ \Delta h = \left( \frac{1}{2\;g} \right) \; \left( 1  \beta^4 \right) \; \left( \frac{ Q }{ C_d \; A_o \; Y } \right)^2  \Delta y }\)  
Symbol  English  Metric 
\(\large{ \Delta h }\) = head loss  \(\large{ ft }\)  \(\large{ m }\) 
\(\large{ g }\) = gravitational acceleration  \(\large{\frac{ft}{sec^2}}\)  \(\large{\frac{m}{s^2}}\) 
\(\large{ \beta }\) (Greek symbol beta) = ratio of pipe inside diameter to orifice diameter  \(\large{ dimensionless }\)  
\(\large{ Q }\) = orifice flow rate  \(\large{\frac{ft^3}{sec}}\)  \(\large{\frac{m^3}{s}}\) 
\(\large{ C_d }\) = orifice discharge coefficient  \(\large{ dimensionless }\)  
\(\large{ A_o }\) = orifice area  \(\large{ in^2 }\)  \(\large{ mm^2 }\) 
\(\large{ Y }\) = expansion coefficient (Y = 1 for incompressible flow)  \(\large{ dimensionless }\)  
\(\large{ \Delta y }\) = elevation change (\(\Delta y = y_1  y_2\))  \(\large{ dimensionless }\)  
Solve for: 

\(\large{ Y = \frac{ C_{d,c} }{ C_{d,i} } }\) \(\large{ C_{d,c} }\) = discharge coefficient compressible fluid \(\large{ C_{d,i} }\) = discharge coefficient incompressible fluid \(\large{ \beta }\) (Greek symbol beta) = \(\frac{d_0}{d_u}\) \(\large{ d_o }\) = orifice or nozzle diameter \(\large{ d_u }\) = upstream pipe inside diameter from orifice or nozzle 
Tags: Head Orifice and Nozzle