While taking a shower, you notice that the shower head is made up of 44 small ro

Question

While taking a shower, you notice that the shower head is made up of 44 small round openings, each with a radius of 2.00 mm. You also determine that it takes 4.00 s for the shower to completely fill a 1.00-liter container you hold in the water stream. The water for the shower is pumped by a pump that is 5.20 m below the level of the shower head. The pump maintains an absolute pressure of 1.50 atm. Use g = 10 m/s2, and assume that 1 atmosphere is 1.0 105 Pa. (a) At what speed does the water emerge from the shower head? (b) What is the speed of the water in the pipe connected to the pump? (c) What is the cross-sectional area of the pipe connected to the pump?

Explanation / Answer

a)

let the speed of water from the shower head is v1

Now , using equation of continuity

v1 * A1 * N = volume flow rate

44 * pi * (0.002)^2 * v1 = 1 *10^-3/4

v1 = 0.452m/s

the speed of water from shower head is 0.497 m/s

b)

let the speed of water is pump is v2

Using bernoull's equation

1.5 * 1.01 *10^5 - 1.01 *10^5 - 1000 * 9.8 * 5.2 = 0.5 * 1000 *(0.452^2 - v2^2)

solving for v2

v2 = 1.06 m/s

the speed of water from the pump is 1.06 m/s

c)

using equation of continuity

A2 * v2 = volume flow rate

1.06 * A2 = 1 *10^-3/4

A2 = 2.36 *10^-4 m^2

the area of new cross section is 2.36 *10^-4 m^2

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.