Water flows at 0.67 m/s through a 3.0 cm diameter hose that terminates in a 0.25

Question

Water flows at 0.67 m/s through a 3.0 cm diameter hose that terminates in a 0.25 cm diameter nozzle. Assume laminar non-viscous steady-state flow.

At what speed does the water pass through the nozzle?
96.48 m/s

If the pump at one end of the hose and the nozzle at the other end are at the same height, and if the pressure at the nozzle is 1 atm, what is the pressure at the pump?

_______________________atm

For the second one, I got 2244376.55, but that was wrong and I do not know what I did wrong. Thanks!

Explanation / Answer

Using the continuity equation A1V1=A2V2 V1=(0.67*3*3)/(0.25*0.25) =96.48 m/s using Bernouli's equation P1/d+V1^2/2+gh=constant P1=d*(V2^2-V1^2)/2+P2 =1000*(96.48^2-0.67^2)/2+100000 Pressure at the pump=4753970.75 Pa =47.53 atm

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