A nozzle has a velocity head at an outlet of 10 m. If the jet is vertical, the height reached by the stream is

Concept:

The velocity of the stream at the nozzle

\(U=\sqrt {2gH} \)

\(H={U^2\over 2g}\)

Equation of motion

V² = U² - 2gh

where U is the initial velocity of the stream at the nozzle, V is the final velocity of the steam, H is the velocity head at the outlet of the nozzle, h is the height reached by the stream, g is the acceleration due to gravity.

Calculation:

Given:

H = 10 m.

The velocity of the stream at the nozzle

\(H={U^2\over 2g}\)

U² = 20 × g

Equation of motion

V2 = U2 - 2gh

Putting the value of U² in the above equation, also the final velocity at height h will be 0 (i.e. v = 0).

20g = 2g × h

h = 10 m

Note: Without any losses, velocity head = the height reached by the stream