Question

A water supply maintains a constant rate of flow for water in a hose. you want to change the opening of the nozzle so that water leaving the nozzle reaches a height that is four times the current maximum height the water reaches with the nozzle vertical. to do so, what should you do?

Answer 1

To make water from a hose reach four times its current maximum height, you should adjust the nozzle to reduce its diameter, which increases the speed of the water due to Bernoulli's Equation and contributes to the water reaching a higher elevation.

Step-by-step explanation:

To change the opening of the nozzle so that the water leaving the nozzle reaches a height that is four times the current maximum height, you would have to adjust the speed of the water coming out of the nozzle. This is due to the concept explained by Bernoulli's Equation, where the increased speed of water coming from a narrower opening leads to greater kinetic energy and the potential to reach a higher elevation.

When you partially cover the opening of a hose with your thumb or adjust the nozzle to decrease the diameter, you are increasing the water's exit velocity due to conservation of mass flow rate and the equation of continuity (the volume flow rate must be constant). High exit velocity combined with the kinetic energy of the water will allow it to reach a greater height.

By decreasing the diameter of the nozzle, you increase the speed of the water, which in turn increases the maximum height the water can reach.

Answer 2

The answer for the problem is explained through this: From V = √(2 g y), the velocity would need to double if the height quadruples. So if we need to double the velocity, the area must be reduce by a factor of 2, assuming producing the same flow rate.