/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 41 A garden hose of inner radius \(... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 41

A garden hose of inner radius \(1.0 \mathrm{cm}\) carries water at $2.0 \mathrm{m} / \mathrm{s} .\( The nozzle at the end has radius \)0.20 \mathrm{cm} .$ How fast does the water move through the nozzle?

Short Answer

Expert verified
Answer: The speed of the water through the nozzle is 25.0 m/s.

Step by step solution

01

Calculate the cross-sectional area of the hose and the nozzle

We can use the formula for the area of a circle to calculate the cross-sectional areas of both the hose and the nozzle by plugging in their respective radii. The area of the hose (\(A_{1}\)) is given by: $$ A_{1} = \pi r_{1}^2 $$ where \(r_1 = 1.0 \text{ cm}\) is the inner radius of the hose. The area of the nozzle (\(A_{2}\)) is given by: $$ A_{2} = \pi r_{2}^2 $$ where \(r_2 = 0.20 \text{ cm}\) is the inner radius of the nozzle.
02

Apply the principle of continuity

According to the principle of continuity, the product of the cross-sectional area and the speed of the fluid should remain constant in the hose and the nozzle. Let \(v_{1}\) be the speed in the hose, and \(v_{2}\) be the speed in the nozzle. $$ A_{1}v_{1} = A_{2}v_{2} $$
03

Plug in the given values and solve for \(v_{2}\)

We are given \(v_{1} = 2.0 \text{ m/s}\) and the inner radii of the hose and the nozzle. Plug in these values and the expressions for \(A_{1}\) and \(A_{2}\) and solve for \(v_{2}\): $$ (\pi r_{1}^2)v_{1} = (\pi r_{2}^2)v_{2} $$ Divide both sides by \(\pi\) and solve for \(v_{2}\): $$ v_{2} = \frac{r_{1}^2}{r_{2}^2}v_{1} $$ $$ v_{2} = \frac{(1.0 \text{ cm})^2}{(0.20 \text{ cm})^2}(2.0 \text{ m/s}) $$
04

Convert units and calculate the speed of the water through the nozzle

Convert the radii to meters before calculating \(v_{2}\): $$ v_{2} = \frac{(0.01 \text{ m})^2}{(0.002 \text{ m})^2}(2.0 \text{ m/s}) $$ Calculate the speed of the water through the nozzle: $$ v_{2} = 25.0 \text{ m/s} $$ The water moves through the nozzle at a speed of \(25.0 \text{ m/s}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Atmospheric pressure is about \(1.0 \times 10^{5} \mathrm{Pa}\) on average. (a) What is the downward force of the air on a desktop with surface area $1.0 \mathrm{m}^{2} ?$ (b) Convert this force to pounds so you really understand how large it is. (c) Why does this huge force not crush the desk?
A house with its own well has a pump in the basement with an output pipe of inner radius \(6.3 \mathrm{mm}\). Assume that the pump can maintain a gauge pressure of \(410 \mathrm{kPa}\) in the output pipe. A shower head on the second floor (6.7 \(\mathrm{m}\) above the pump's output pipe) has 36 holes, each of radius \(0.33 \mathrm{mm} .\) The shower is on "full blast" and no other faucet in the house is open. (a) Ignoring viscosity, with what speed does water leave the shower head? (b) With what speed does water move through the output pipe of the pump?
An IV is connected to a patient's vein. The blood pressure in the vein has a gauge pressure of \(12 \mathrm{mm}\) Hg. At least how far above the vein must the IV bag be hung in order for fluid to flow into the vein? Assume the fluid in the IV has the same density as blood.
A stone of weight \(W\) has specific gravity \(2.50 .\) (a) When the stone is suspended from a scale and submerged in water, what is the scale reading in terms of its weight in air? (b) What is the scale reading for the stone when it is submerged in oil (specific gravity \(=0.90\) )?

The average density of a fish can be found by first weighing it in air and then finding the scale reading for the fish completely immersed in water and suspended from a scale. If a fish has weight \(200.0 \mathrm{N}\) in air and scale reading \(15.0 \mathrm{N}\) in water, what is the average density of the fish?
See all solutions

Recommended explanations on Physics Textbooks

Measurements

Read Explanation

Radiation

Read Explanation

Medical Physics

Read Explanation

Mechanics and Materials

Read Explanation

Energy Physics

Read Explanation

Atoms and Radioactivity

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.