/*! 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 113 A uniform jet of water leaves a ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 113

A uniform jet of water leaves a 15 -mm-diameter nozzle and flows directly downward. The jet speed at the nozzle exit plane is \(2.5 \mathrm{m} / \mathrm{s}\). The jet impinges on a horizontal disk and flows radially outward in a flat sheet. Obtain a general expression for the velocity the liquid stream would reach at the level of the disk. Develop an expression for the force required to hold the disk stationary, neglecting the mass of the disk and water sheet. Evaluate for \(h=3 \mathrm{m}\).

Short Answer

Expert verified
The velocity the liquid stream would reach at the level of the disk is expressed by \(v_r = Q/(2 \pi r h)\). The force required to hold the disk stationary is given by \(F = \rho Q (V_2 - V_1)\).

Step by step solution

01

Calculate the Exit Jet Velocity

We know that the exit jet velocity is given by \(V_2 = \sqrt{2gh + v_1^2}\) where \(g\) is the acceleration due to gravity (9.8 m/s^2), \(h\) is the height (3m) and \(v_1\) is the initial jet speed (2.5 m/s).
02

Calculate the Volume Flow Rate

The volume flow rate \(Q\) of the water can be calculated using the formula \(Q = Av\) where \(A\) is the cross-sectional area of the nozzle and \(v\) is the velocity. The cross-sectional area can be calculated as \(A = \pi d^2/4\) where \(d\) is the diameter of the nozzle (0.015m). Substituting these values we get \(Q = Av = \pi (0.015m)^2/4 \times 2.5m/s\).
03

Express the Radial Velocity in Terms of Radius

The radial velocity \(v_r\) at any radius \(r\) from the center of the disk can be expressed as \(v_r = Q/(2 \pi r h)\). This is obtained from the principle of conservation of mass.
04

Calculate the Force

The force \(F\) required to hold the disk stationary can be calculated using the formula \(F = \rho Q (V_2 - V_1)\) where \(\rho\) is the density of water. With the known values, calculate \(F\).

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

\(\mathrm{A}\) high school experiment consists of a block of mass \(2 \mathrm{kg}\) sliding across a surface (coefficient of friction \(\mu=0.6\) ). If it is given an initial velocity of \(5 \mathrm{m} / \mathrm{s}\), how far will it slide, and how long will it take to come to rest? The surface is now roughened a little, so with the same initial speed it travels a distance of \(2 \mathrm{m}\). What is the new coefficient of friction, and how long does it now slide?

A horizontal axisymmetric jet of air with 0.5 in. diameter strikes a stationary vertical disk of 8 in. diameter. The jet speed is 225 ft/s at the nozzle exit. A manometer is connected to the center of the disk. Calculate (a) the deflection, \(h,\) if the manometer liquid has \(S G=1.75\) and (b) the force exerted by the jet on the disk.

Consider the steady adiabatic flow of air through a long straight pipe with \(0.05 \mathrm{m}^{2}\) cross-sectional area. At the inlet, the air is at \(200 \mathrm{kPa}\) (gage), \(60^{\circ} \mathrm{C}\), and has a velocity of \(150 \mathrm{m} / \mathrm{s}\). At the exit, the air is at \(80 \mathrm{kPa}\) and has a velocity of \(300 \mathrm{m} / \mathrm{s}\). Calculate the axial force of the air on the pipe. (Be sure to make the direction clear.)

Oil flows steadily in a thin layer down an inclined plane. The velocity profile is \\[ u=\frac{\rho g \sin \theta}{\mu}\left[h y-\frac{y^{2}}{2}\right] \\] Express the mass flow rate per unit width in terms of \(\rho, \mu, g\) \(\theta,\) and \(h\)

At rated thrust, a liquid-fueled rocket motor consumes \(80 \mathrm{kg} / \mathrm{s}\) of nitric acid as oxidizer and \(32 \mathrm{kg} / \mathrm{s}\) of aniline as fuel. Flow leaves axially at \(180 \mathrm{m} / \mathrm{s}\) relative to the nozzle and at \(110 \mathrm{kPa}\). The nozzle exit diameter is \(D=0.6 \mathrm{m}\). Calculate the thrust produced by the motor on a test stand at standard sealevel pressure.
See all solutions

Recommended explanations on Physics Textbooks

Measurements

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation

Astrophysics

Read Explanation

Radiation

Read Explanation

Oscillations

Read Explanation

Rotational Dynamics

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.