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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 pressure-reducing 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

$$\Delta h \;=\; ( 1 \;/\; 2\;g ) \; ( 1 - \beta^4 ) \; ( Q \;/\; C_d \; A_o \; Y )^2$$     (Horizontal Orifice and Nozzle Head Loss)

$$g \;=\; ( 1 \;/\; 2\;\Delta h ) \; ( 1 - \beta^4 ) \; ( Q \;/\; C_d \; A_o \; Y )^2$$

$$\beta \;=\; \sqrt[4]{ 1 - 2 \; g \; \Delta h \; \sqrt{ Q \;/\; C_d \; A_o \; Y } }$$

$$Q \;=\; \Delta h \; ( 2 \; g \;/\; 1 − b^4 ) \; ( Cd \; Ao \; Y )^2$$

$$Cd \;=\; ( 1 \;/\; Ao \; Y ) \; (1 \;/\; \sqrt{ 2 \; g \;/\; 1 − b^4 \; Q } \;\; )$$

$$Ao \;=\; \sqrt{ 1 − b^4 \; Q \;/\; \Delta h \; 2 \; g } \;/\; Cd \; Y$$

$$Y \;=\; \sqrt{ 1 − b^4 \; Q \;/\; \Delta h } \;/\; Cd \; Ao$$

### Solve for Δh

 gravitational acceleration, g pipe ID to orifice diameter, β orifice flow rate, Q orifice discharge coefficient, Cd orifice area, Ao expansion coefficient, Y

### Solve for g

 head loss, Δh pipe ID to orifice diameter, β orifice flow rate, Q orifice discharge coefficient, Cd orifice area, Ao expansion coefficient, Y

### Solve for β

 gravitational acceleration, g head loss, Δh orifice flow rate, Q orifice discharge coefficient, Cd orifice area, Ao expansion coefficient, Y

### Solve for Q

 head loss, Δh gravitational acceleration, g pipe ID to orifice diameter, β orifice discharge coefficient, Cd orifice area, Ao expansion coefficient, Y

### Solve for Cd

 orifice area, Ao expansion coefficient, Y gravitational acceleration, g pipe ID to orifice diameter, β orifice flow rate, Q

### Solve for Ao

 pipe ID to orifice diameter, β orifice flow rate, Q head loss, Δh gravitational acceleration, g orifice discharge coefficient, Cd expansion coefficient, Y

### Solve for Y

 pipe ID to orifice diameter, β orifice flow rate, Q head loss, Δh orifice discharge coefficient, Cd orifice area, Ao

Symbol English Metric
$$\Delta h$$ = head loss $$ft$$ $$m$$
$$g$$ = gravitational acceleration  $$ft \;/\; sec^2$$ $$m \;/\; s^2$$