To clean the outside of your house you rent a small high-pressure water sprayer. The sprayer's pump delivers slow-moving water at a pressure of 9000000.0 Pa (about 90.0 atmospheres). How fast can this water move if all of its pressure potential energy becomes kinetic energy as it flows through the nozzle of the sprayer?

Velocity is 134.16 m/s

Explanation:

Slow moving water pressure is the dynamic pressure. Dynamic pressure is actually the kinetic energy per unit volume of a fluid particle. It is equal to the difference between stagnation pressure and static pressure and also can be derived from Bernoulli's equation.

Formula for Dynamic Pressure (P) is

P = 0.5 d v²

Where d is density of fluid and v is the velocity.

Density of water = 1000 kg/m³

P = 9000000 Pa

V = ?

P = 0.5 d v²

9000000 = 0.5 * 1000 * v²

v = √ (9000000 : 500)

v = 134.16 m/s