This article provides calculation methods for correlating design, flow rate and pressure loss as a fluid passes through a nozzle or orifice. Nozzles and orifices are often used to deliberately reduce pressure, restrict flow or to measure flow rate.

1. Air Flow Through Slot
2. Flow Rate Through Slot
3. Water Flow Through A Slot
4. Flow Through A Slot
5. Flow Through A Rectangular Slot

Subscripts

Air was sucked through the tunnel and through a slot by a -h.p. Blower, the pipe system being so arranged that the total rate of flow upstream of the slot and the rate of flow through the slot could be measured separately. The rate of flow throug5 the slot was measured with a plate. Slot: noun a narrow opening or groove: slit, notch. A narrow passage or enclosure. A passage through the wing of an airplane or of a missile that is located usually near the leading edge and formed between a main and an auxiliary airfoil for improving flow conditions over the wing so as to increase lift and delay stalling of the wing. Much greater than the depth of flow is a good approximation to a flow with infinite width. 8 Take the x direction to be downstream and the y direction to be normal to the boundary, with y = 0 at the bottom of the flow (Figure 4-1). An orifice plate is a thin plate with a hole in it, which is usually placed in a pipe. When a fluid (whether liquid or gaseous) passes through the orifice, its pressure builds up slightly upstream of the orifice but as the fluid is forced to converge to pass through the hole, the velocity increases and the fluid pressure decreases.

In the case of a simple concentric restriction orifice the fluid is accelerated as it passes through the orifice, reaching the maximum velocity a short distance downstream of the orifice itself (the Vena Contracta). The increase in velocity comes at the expense of fluid pressure resulting in low pressures in the Vena Contracta. In extreme cases this may lead to cavitation when the local pressure is less than the vapour pressure of a liquid.

Downstream of the Vena Contracta in the recovery zone, the fluid decelerates converting excess kinetic energy into pressure as it slows. When the fluid has decelerated and returned to the normal bulk flow pattern the final downstream pressure has been reached.

The discharge coefficientcharacterises the relationship between flow rate and pressure loss based on the geometry of a nozzle or orifice. You can find typical values in our article on discharge coefficients for nozzles and orifices.

The relationships for flow rate, pressure loss and head loss through orifices and nozzles are presented in the subsequent section. These relationships all utilise the parameter, the ratio of orifice to pipe diameter which is defined as:

Where the point downstream of the orifice is sufficiently far away that the fluid has returned to normal full pipe velocity profile.

Horizontal Orifices and Nozzles

For orifices and nozzles installed in horizontal pipework where it can be assumed that there is no elevation change, head loss and flow rate may be calculated as follows:

Vertical Orifices and Nozzles

For orifices and nozzles installed in vertical piping, with elevation change, the following head loss and flow rate equations may be used:

Expansion Coefficient

Air Flow Through Slot

The expansion coefficient takes account of the difference between the discharge coeffcicient for compressible and incompressible flows. It is defined as:

Flow Rate Through Slot

The expansion factoris typically determined empirically and can be calculated using one of the formulas below.

For incompressible fluids:

American Gas Association method as described in AGA 3.1:

Water Flow Through A Slot

International Standards Organistion method as described in ISO 5167-2:

Flow Through A Slot

Flow Through A Rectangular Slot