Question

A pipe with a diameter of 4 centimeters is attached to a garden hose with a nozzle. If the velocity of flow in the pipe is 2m/s, what is the velocity of the flow at the nozzle when it is adjusted to have a diameter of 1 centimeters?

Answer 1

Answer:

Use equation of continuity as

A_1v_1=A_2v_2A1v1=A2v2

Here, A_1A1 is the enter area of the pipe, A_2A2 is the water exit area of the pipe and v_1v1 is the velocity of flow in the pipe.

Given v_1=2m/s,A_1=\pi(1cm)^2,A_2=\pi(0.2cm)^2v1=2m/s,A1=π(1cm)2,A2=π(0.2cm)2

substitute the given values, we get

2m/s\times\pi (1cm)^2=v_2\times\pi\times(0.2cm)^22m/s×π(1cm)2=v2×π×(0.2cm)2

v_2=\frac{2m/s\times(1\times10^-^2m)^2}{(0.2\times10^-^2m)^2}

v_2=50m/sv2=50m/s

Thus, velocity of the flow at the nozzle when it is adjusted is 50 m/s.

#Learn More: equation of continuity.

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