Simple garden hoses generate higher velocities that help remove dirt and grime from our automobiles. The same fluid dynamics principles that are used with the garden hose can also be used to generate pressures high enough to cut metal using a modern water jet machine.
What is the exit velocity and inlet pressure for the water flowing through the nozzle? Average fluid properties are given. Frictional/shear stresses are negligible and the fluid is incompressible.
There are two unknowns, the inlet pressure and the exit velocity. Therefore two equations are needed. The possible equations include: 1) conservation of mass, 2) conservation of energy, and 3) momentum. In this problem, the conservation of mass and Bernoulli’s equation (momentum) will be used. Note that the flow is steady state, the fluid is incompressible and inviscid since the frictional/shear stresses are negligible. These three criteria make the use of Bernoulli’s equation acceptable.
The conservation of mass equation for a single input-single output system can be written as
Since the fluid is incompressible, the densities cancel and the above equation become
Solving for the exit velocity yields
Bernoulli’s equation for a streamline starting at the inlet and ending at the exit is
Since there is no elevation change, this equation reduces to
Solving for the inlet pressure yields
Learn how to apply Bernoulli’s equation to solve practical fluid dynamics problems.