Water is being sprayed from a nozzle at the end of a garden hose of diameter 2.0 cm.If the nozzle has an opening of diameter 0.50 cm,and if the water leaves the nozzle at a speed of 15 m/s,what is the speed of the water inside the hose?
A) 0.63 m/s
B) 0.94 m/s
C) 2.5 m/s
D) also 10 m/s

Question

Quizplus · Accepted Answer

We can use the equation of continuity to solve this problem:

A1V1 = A2V2

where A1 and V1 are the cross-sectional area and velocity of the water inside the hose, and A2 and V2 are the corresponding values at the nozzle opening.

We can first calculate the cross-sectional area of the hose:

A1 = πr1^2 = π(0.01 m)^2 = 3.14 x 10^-4 m^2

where r1 is the radius of the hose (which is half of its diameter).

We can then calculate the cross-sectional area of the nozzle opening:

A2 = πr2^2 = π(0.0025 m)^2 = 1.96 x 10^-5 m^2

where r2 is the radius of the nozzle opening.

We are given V2 = 15 m/s. Substituting these values into the equation of continuity, we can solve for V1:

V1 = (A2/A1) V2 = (1.96 x 10^-5 m^2 / 3.14 x 10^-4 m^2) x 15 m/s ≈ 0.94 m/s

Therefore, the speed of water inside the hose is 0.94 m/s.

Water Is Being Sprayed from a Nozzle at the End