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 3.00 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 5.70 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?

To solve the problem it is necessary to apply the concepts related to the calculation of discharge flow, Bernoulli equations and energy conservation in incompressible fluids.

PART A) For the calculation of the velocity we define the area and the flow, thus

At the same time the rate of flow would be

By definition the discharge is expressed as

Where,

A= Area

v = velocity

N = Number of exits

Q = NAv

Re-arrange to find v,

PART B) From the continuity equations formulated by Bernoulli we can calculate the speed of water in the pipe

Replacing with our values we have that

PART C) Assuming that water is an incomprehensible fluid we have to,

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.