/*! 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 76 A horizontal axisymmetric jet of... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 76

A horizontal axisymmetric jet of air with 0.4 in. diameter strikes a stationary vertical disk of 7.5 in. diameter. The jet speed is \(225 \mathrm{ft} / \mathrm{s}\) at the nozzle exit. A manometer is connected to the center of the disk. Calculate (a) the deflection, if the manometer liquid has \(\mathrm{SG}=1.75,(\mathrm{b})\) the force exerted by the jet on the disk, and (c) the force exerted on the disk if it is assumed that the stagnation pressure acts on the entire forward surface of the disk. Sketch the streamline pattern and plot the distribution of pressure on the face of the disk.

Short Answer

Expert verified
Jet is causing the fluid in the manometer to deflect by a certain amount. Forces exerted on the disk by the jet and by considering the stagnation pressure acting over the whole area were computed. The streamline pattern of the flow and the distribution of pressure on the disk's surface were also visually represented. Critical thinking and application of fluid dynamics principles were crucial in solving this problem.

Step by step solution

01

Calculate the Deflection

The deflection in the manometer is given by \( \Delta h = \frac{v^{2}}{2g} \frac{1}{SG - 1} \), where v is the velocity of air, g is the acceleration due to gravity and SG is the specific gravity of the manometer liquid. Given \( v = 225 ft/s, SG = 1.75 \) and \( g = 32.2 ft/s^2 \), substitute these values in to get the deflection.
02

Calculate the Force Exerted by the Jet on the Disk

The force exerted by the jet is given by F = \(\rho Q v \), where 蟻 is the density of the air, Q is the volumetric flow rate of the air, and v is the velocity of air. We know \( 蟻 = 0.002378 slug/ft^3 \) and V = \( \pi (D^2)/4 \times v \), where D is the jet diameter. Substitute the given and computed values into the formula to find F.
03

Calculate the Force considering Stagnation Pressure

The force when considering the stagnation pressure is F = P_s 脳 A where P_s is the stagnation pressure and A is the area of the disk. P_s = \( 蟻v^2/2 + 蟻gh\) where h is the height above some reference point (we can take h as zero here as there is no such height specified). The area A is \( \pi (D^2)/4 \) where D is the diameter of the disk. Substitute the values into the formulas to find F.
04

Sketch the Streamline Pattern and Plot the Pressure Distribution

The streamline pattern can be sketched by following the motion of the air particles from the jet nozzle to the disk. The pressure distribution on the face of the disk can be plotted by considering points along the radius of the disk and evaluating the pressure at these points using the Bernoulli's equation. Keep in mind that pressure would be highest at the center and would decrease as we move towards the edge.

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

Describe the pressure distribution on the exterior of a multistory building in a steady wind. Identify the locations of the maximum and minimum pressures on the outside of the building. Discuss the effect of these pressures on infiltration of outside air into the building.

Water flows at low speed through a circular tube with inside diameter of 2 in. A smoothly contoured body of 1.5 in. diameter is held in the end of the tube where the water discharges to atmosphere. Neglect frictional effects and assume uniform velocity profiles at each section. Determine the pressure measured by the gage and the force required to hold the body.

Consider the flow field with velocity given by \(\vec{V}=\left[A\left(y^{2}-x^{2}\right)-B x | \hat{i}+[2 A x y+B y] \hat{j}, A=1 \mathrm{ft}^{-1} \cdot \mathrm{s}^{-1}, B=1\right.\) \(\mathrm{ft}^{-1} \cdot \mathrm{s}^{-1} ;\) the coordinates are measured in feet. The density is \(2 \operatorname{slug} / \mathrm{ft}^{3},\) and gravity acts in the negative \(y\) direction. Calculate the acceleration of a fluid particle and the pressure gradient at point \((x, y)=(1,1)\)

A diffuser for an incompressible, inviscid fluid of density \(\rho=1000 \mathrm{kg} / \mathrm{m}^{3}\) consists of a diverging section of pipe. At the inlet the diameter is \(D_{i}=0.25 \mathrm{m},\) and at the outlet the diameter is \(D_{o}=0.75 \mathrm{m} .\) The diffuser length is \(L=1 \mathrm{m},\) and the diameter increases linearly with distance \(x\) along the diffuser. Derive and plot the acceleration of a fluid particle, assuming uniform flow at each section, if the speed at the inlet is \(V_{i}=5 \mathrm{m} / \mathrm{s}\). Plot the pressure gradient through the diffuser, and find its maximum value. If the pressure gradient must be no greater than \(25 \mathrm{kPa} / \mathrm{m}\), how long would the diffuser have to be?

\(\mathrm{A}\) source and a sink with strengths of equal magnitude, \(q=3 \pi \mathrm{m}^{2} / \mathrm{s},\) are placed on the \(x\) axis at \(x=-a\) and \(x\) \(=a,\) respectively. A uniform flow, with speed \(U=20 \mathrm{m} / \mathrm{s},\) in the positive \(x\) direction, is added to obtain the flow past a Rankine body. Obtain the stream function, velocity potential, and velocity field for the combined flow. Find the value of \(\psi=\) constant on the stagnation streamline. Locate the stagnation points if \(a=0.3 \mathrm{m}\)
See all solutions

Recommended explanations on Physics Textbooks

Fields in Physics

Read Explanation

Magnetism

Read Explanation

Particle Model of Matter

Read Explanation

Fluids

Read Explanation

Space Physics

Read Explanation

Work Energy and Power

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.