/*! 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 103 Air enters a duct, of diameter \... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 103

Air enters a duct, of diameter \(D=25.0 \mathrm{mm},\) through a well-rounded inlet with uniform speed, \(U_{1}=0.870 \mathrm{m} / \mathrm{s}\) At a downstream section where \(L=2.25 \mathrm{m},\) the fully developed velocity profile is \\[ \frac{u(r)}{U_{c}}=1-\left(\frac{r}{R}\right)^{2} \\] The pressure drop between these sections is \(p_{1}-p_{2}=1.92 \mathrm{N} /\) \(\mathrm{m}^{2}\), Find the total force of friction exerted by the tube on the air.

Short Answer

Expert verified
The total force of friction exerted by the tube on the air is \(0.000941 \, N\).

Step by step solution

01

Calculate the Radius

First, we calculate the radius of the duct, which will be used later on in the velocity profile equation. The radius \(R\) is half of the diameter \(D\), thus \(R = D / 2 = 25.0 \, mm / 2 = 12.5 \, mm = 0.0125 \, m\).
02

Identify the Average Speed

Then, we identify the average speed \(U_c\) from the problem. We are told that the uniform speed \(U_{1}\) is \(0.870 \, m/s\). Since for fully developed laminar flow in a circular duct the average speed equals the maximum speed divided by 2, \(U_c = U_{1} / 2 = 0.870 \, m/s / 2 = 0.435 \, m/s\). This equation can be derived from the velocity profile given in the problem.
03

Determine the Pressure Drop

We then use the pressure drop \(dp = p_{1} - p_{2} = 1.92 \, N/m^{2}\) provided in the problem. This value will be used in the force equation we formulate below.
04

Calculate the Total Force of Friction

Finally, we can calculate the total force of friction exerted by the tube on the air. The force of friction \(F\) can be calculated by multiplying the pressure drop \(dp\) by the area \(A\) of the duct. The area \(A\) of a circle is given by \(\pi r^{2}\). Therefore, we can calculate \(A = \pi * (0.0125 \, m)^{2} = 0.00049 \, m^{2}\), and then substitute these values into the force equation \(F = dp * A = 1.92 \, N/m^{2} * 0.00049 \, m^{2} = 0.000941 \, N\).

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

A centrifugal water pump with a 0.1-m-diameter inlet and a 0.1 -m-diameter discharge pipe has a flow rate of \(0.02 \mathrm{m}^{3} / \mathrm{s}\). The inlet pressure is \(0.2 \mathrm{m}\) Hg vacuum and the exit pressure is \(240 \mathrm{kPa}\). The inlet and outlet sections are located at the same elevation. The measured power input is \(6.75 \mathrm{kW}\). Determine the pump efficiency.

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 flow through the sudden expansion shown. If the flow is incompressible and friction is neglected, show that the pressure rise, \(\Delta p=p_{2}-p_{1},\) is given by \\[ \frac{\Delta p}{\frac{1}{2} \rho \bar{V}_{1}^{2}}=2\left(\frac{d}{D}\right)^{2}\left[1-\left(\frac{d}{D}\right)^{2}\right] \\] Plot the nondimensional pressure rise versus diameter ratio to determine the optimum value of \(d / D\) and the corresponding value of the nondimensional pressure rise. Hint. Assume the pressure is uniform and equal to \(p_{1}\) on the vertical surface of the expansion.

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 \(h\)

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.)
See all solutions

Recommended explanations on Physics Textbooks

Particle Model of Matter

Read Explanation

Fundamentals of Physics

Read Explanation

Quantum Physics

Read Explanation

Radiation

Read Explanation

Energy Physics

Read Explanation

Scientific Method Physics

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.