/*! 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 46 An open-circuit wind tunnel draw... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 46

An open-circuit wind tunnel draws in air from the atmosphere through a well- contoured nozzle. In the test section, where the flow is straight and nearly uniform, a static pressure tap is drilled into the tunnel wall. A manometer connected to the tap shows that static pressure within the tunnel is \(45 \mathrm{mm}\) of water below atmospheric. Assume that the air is incompressible, and at \(25^{\circ} \mathrm{C}, 100 \mathrm{kPa}\) (abs). Calculate the air speed in the wind-tunnel test section.

Short Answer

Expert verified
The air speed in the wind-tunnel test section is approximately \(27 m/s\).

Step by step solution

01

Convert pressure difference to Pascal

Given that the pressure difference is 45 mm of water, we know 1 mm of water is equivalent to 9.80665 Pascals. So, the pressure difference in Pascal is \( 45 \, mm \, H_{2}O \times 9.80665 \, \frac{Pa}{mm \, H_{2}O} \approx 441 \, Pa \).
02

Calculate air density

Air density can be calculated by using the ideal gas law \(蟻 = \frac{P}{RT}\), where \(P = 100 \, kPa = 100000 \, Pa\) is the atmospheric pressure, \(R = 287 \, J/(kg \cdot K)\) is the specific gas constant for dry air, and \(T = 25^{\circ}C + 273.15 = 298.15 K\) is the absolute temperature. Substitute these values into the equation and calculate to find \(蟻 \approx 1.184 \, kg/m^3\).
03

Calculate air speed

Now, apply Bernoulli's theorem on a streamline from the free stream outside the wind tunnel to the test section, \(P_{0} = P_{1} + \frac{1}{2} \rho v^{2}\). Rearranging the equation we get, \(v = \sqrt{\frac{2 (P_{0}-P_{1})}{\rho}}\), substitute \(P_{0} - P_{1} = 441 Pa\) and \(蟻 = 1.184 kg/m^3\) into the equation, therefore, the air speed \(v \approx 27 m/s\).

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

Water flows in a circular duct. At one section the diameter is \(0.3 \mathrm{m}\), the static pressure is \(260 \mathrm{kPa}\) (gage), the velocity is \(3 \mathrm{m} / \mathrm{s},\) and the elevation is \(10 \mathrm{m}\) above ground level. At a section downstream at ground level, the duct diameter is \(0.15 \mathrm{m}\) Find the gage pressure at the downstream section if frictional effects may be neglected.

Consider the flow field formed by combining a uniform flow in the positive \(x\) direction and a source located at the origin. Let \(U=30 \mathrm{m} / \mathrm{s}\) and \(q=150 \mathrm{m}^{2} / \mathrm{s} .\) Plot the ratio of the local velocity to the freestream velocity as a function of \(\theta\) along the stagnation streamline. Locate the points on the stagnation streamline where the velocity reaches its maximum value. Find the gage pressure there if the fluid density is \(1.2 \mathrm{kg} / \mathrm{m}^{3}\)

Consider the flow represented by the stream function \(\psi=A x^{2} y,\) where \(A\) is a dimensional constant equal to 2.5 \(\mathrm{m}^{-1} \cdot \mathrm{s}^{-1}\). The density is \(1200 \mathrm{kg} / \mathrm{m}^{3}\). Is the flow rotational? Can the pressure difference between points \((x, y)=(1,4)\) and (2,1) be evaluated? If so, calculate it, and if not, explain why.

Consider the flow field presented by the potential function $\phi=x^{5}-10 x^{3} y^{2}+5 x y^{4}-x^{2}+y^{2} .$ Verify that this is an incompressible flow, and obtain the corresponding stream function.

The velocity field for a plane vortex sink is given by \(\vec{V}=(-q / 2 \pi r) \hat{e}_{r}+(K / 2 \pi r) \hat{e}_{\theta}, \quad\) where \(\quad q=2 \quad \mathrm{m}^{3} / \mathrm{s} / \mathrm{m} \quad\) and \(K=1 \mathrm{m}^{3} / \mathrm{s} / \mathrm{m} .\) The fluid density is \(1000 \mathrm{kg} / \mathrm{m}^{3} .\) Find the acceleration at \((1,0),(1, \pi / 2),\) and \((2,0) .\) Evaluate \(\nabla p\) under the same conditions.
See all solutions

Recommended explanations on Physics Textbooks

Mechanics and Materials

Read Explanation

Solid State Physics

Read Explanation

Electric Charge Field and Potential

Read Explanation

Torque and Rotational Motion

Read Explanation

Electromagnetism

Read Explanation

Translational 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.