Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 9: Problem 51

For small Reynolds number flows, the drag coefficient of an object is given by a constant divided by the Reynolds number (see Table 9.4 . Thus, as the Reynolds number tends to zero, the drag coefficient becomes infinitely large. Does this mean that for small velocities (hence, small Reynolds numbers) the drag is very large? Explain.

Short Answer

Expert verified
No, the drag is not very large for small velocities. Even though the drag coefficient becomes infinitely large as the Reynolds number decreases, the overall drag decreases due to the smaller square of velocity in the drag force equation.

Step by step solution

01

Analysis of the given

We know from the question that the drag coefficient (\(C_d\)) is a constant over the Reynolds number (Re) and the drag coefficient becomes infinitely large as the Reynolds number tends to zero.
02

Understanding the logic behind the question

What we need to deduce here is about drag and not the drag coefficient. Now, it might sound intuitive that larger the drag coefficient, more the drag. However, this is incorrect. The drag on an object is determined by the drag force equation which includes both the drag coefficient and the Reynolds number.
03

Formulating the Solution

The drag force equation is given by \(F_d = C_d * 0.5 * \rho * U^2 * A\), where \(\rho\) is the fluid density, \(U\) is the flow velocity and \(A\) is the cross-sectional area. Now, for smaller velocities (hence, smaller Reynolds numbers), even though the drag coefficient becomes infinitely large, the square of the velocity becomes closer to zero. Since \(U^2\) is in the drag force equation, it means the overall drag force decreases as velocity decreases, not the other way around. It shows that the drag does not become large for small Reynolds numbers.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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 2 -mm-diameter meteor of specific gravity 2.9 has a speed of \(6 \mathrm{km} / \mathrm{s}\) at an altitude of \(50,000 \mathrm{m}\) where the air density is \(1.03 \times\) \(10^{-3} \mathrm{kg} / \mathrm{m}^{3} .\) If the drag coefficient at this large Mach number condition is \(1.5,\) determine the deceleration of the meteor

Commercial airliners normally cruise at relatively high altitudes \((30,000 \text { to } 35,000 \mathrm{ft}) .\) Discuss how flying at this high altitude (rather than \(10,000 \mathrm{ft}\), for example) can save fuel costs.

An automobile engine has a maximum power output of \(70 \mathrm{hp},\) which occurs at an engine speed of \(2200 \mathrm{rpm} . \mathrm{A} 10 \%\) power loss occurs through the transmission and differential. The rear wheels have a radius of 15.0 in. and the automobile is to have a maximum speed of 75 mph along a level road. At this speed, the power absorbed by the tires because of their continuous deformation is 27 hp. Find the maximum permissible drag coefficient for the automobile at this speed. The car's frontal area is \(24.0 \mathrm{ft}^{2}\)

As is discussed in Section \(9.3,\) the drag on a rough golf ball may be less than that on an equal-sized smooth ball. Does it follow that a 10 -m-diameter spherical water tank resting on a \(20-\mathrm{m}\) -tall support should have a rough surface so as to reduce the moment needed at the base of the support when a wind blows? Explain.

A full-sized automobile has a frontal area of \(24 \mathrm{ft}^{2},\) and a compact car has a frontal area of \(13 \mathrm{ft}^{2}\). Both have a drag coefficient of 0.5 based on the frontal area. Find the horsepower required to move each automobile along a level road in still air at 55 mph. Assume that the power required to deform the tires continuously at this speed (called rolling resistance) is equal to the power to overcome the air resistance. Estimate the gas mileage of both automobiles if the energy supplied to the drive wheels is \(\frac{1}{4}\) that available in the fuel. A gallon of fuel has \(1.0 \times 10^{8} \mathrm{ft} \cdot 1 \mathrm{b}\) available energy.
See all solutions

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

Read Explanation

Work Energy and Power

Read Explanation

Electricity and Magnetism

Read Explanation

Rotational Dynamics

Read Explanation

Mechanics and Materials

Read Explanation

Physical Quantities And Units

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.

Sign-up for free