Calculate the maximum height to which water could be squirted with the hose in E

Question

Calculate the maximum height to which water could be squirted with the hose in Example 12.2 example if it: (a) Emerges from the nozzle with a velocity of 25.5 m/s

Your answer should have units of meters.

Example 12.2 Calculating Fluid Speed: Speed Increases When a Tube Narrows

Information from example 12.2

A nozzle with a radius of 0.250 cm is attached to a garden hose with a radius of 0.900 cm. The flow rate through hose and nozzle is 0.500 L/s.

The speed of the water in the hose is 1.96 m/s and in the nozzle is 25.5 m/s

Explanation / Answer

The velocity head i.e. (v^2/2g) gets converted into elevation head i.e. z

so z= (v^2/2g)= 25.5^2/(2*9.81)=33.14 m

alternatively,

you may consider projectile motion where maximum height attained = (vsinx)^2/(2*g)
for absolute maximum height x=90 and sinx=1
Therefore maximum height attained= (v^2/2g)=33.14m

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