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Exit Spout Velocity Calculator
Hydrostatic pressure will impart a velocity to an exiting fluid jet. The velocity and flowrate of the jet depend on the depth of the fluid.

To calculate the jet velocity and flowrate, enter the parameters below. (The default calculation is for a small tank containing water 20 cm deep, with answers rounded to 3 significant figures. Any interaction of the fluid jet with air is ignored.)

Inputs
  Depth of spout, Dz:    
  Fluid density, r:    
  Spout exit diameter, D:    
  Discharge Coefficient, C:    
Answers
  Exit Velocity, V:  1.98  m/s
  Volume Flowrate:  0.152  l/s
  Mass Flowrate:  0.152  kg/s
 
Equations used in the Calculation
For low-viscosity incompressible fluids such as water, the incompressible Bernoulli equation describes the flow. Applying this equation to a "streamline" that starts at the top free surface and exits out the spout yields,
Note that the exiting fluid jet experiences the same pressure as the free surface (patm). Solving for the fluid jet velocity gives,
The non-zero viscosity of fluids will rob the flow of mechanical energy (converting it into heat within boundary layers hugging the spout walls), hence the fluid jet beyond the spout exit will have a slightly smaller diameter than that of the spout. This factor can be accounted for by a discharge coefficient C, whose value is typically between 0.90 and 0.98. The volumetric flowrate Q results from multiplying the jet velocity times the cross-sectional area,