A garden has an internal diameter of 2.0cm. The diameter of its nozzle is 0.8cm. Assuming that the speed of water in the hose is 0.35m/s, what will be the speed through the nozzle?

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Answer 1 · 2018-05-31T15:06:02

The speed in the nozzle is #=2.1875ms^-1#

The flow rate #=Q m^3s^-1# is constant in the hose and in the nozzle.

The cross section area of the hose is #a_1=pid_1^2/4#

#d_1=2*10^-2m#

#a_1=pi(2*10^-2)^2/4m^2#

The speed in the hose is #u=0.35ms^-1#

Therefore,

#Q=pi(2*10^-2)^2/4*0.35m^3s^-1#

The cross section area of the nozzle is #a_2=pid_2^2/4#

#d_2=0.8*10^-2m#

#a_1=pi(0.8*10^-2)^2/4m^2#

The speed in the hose is #vms^-1#

Therefore,

#Q=pi(0.8*10^-2)^2/4*um^3s^-1#

So,

#pi(2*10^-2)^2/4*0.35=pi(0.8*10^-2)^2/4*u#

#=>#, #u=0.35*(2*10^-2)^2/(0.8*10^-2)^2=2.1875ms^-1#

The speed in the nozzle is #=2.1875ms^-1#