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Refer to Exercise 10 in Section 3.2. Assume that ? = 35.2

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 21E Chapter 3.4

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 21E

Refer to Exercise 10 in Section 3.2. Assume that τ = 35.2 ± 0.1 Pa, h = 12.0 ± 0.3 mm, and μ = 1.49 Pa · s with negligible uncertainty. Estimate V, and find the relative uncertainty in the estimate.

Exercise 10: In a Couette flow, two large flat plates lie one on top of another, separated by a thin layer of fluid. If a shear stress is applied to the top plate, the viscosity of the fluid produces motion in the bottom plate as well. The velocity V in the top plate relative to the bottom plate is given by V = τh/μ, where τ is the shear stress applied to the top plate, h is the thickness of the fluid layer, and μ is the viscosity of the fluid. Assume that μ = 1.49 Pa • s and h = 10 mm, both with negligible uncertainty.

a. Suppose that τ = 30.0 ± 0.1 Pa. Estimate V, and find the uncertainty in the estimate.

b. If it is desired to estimate V with an uncertainty of 0.2 mm/s, what must be the uncertainty in τ?

Step-by-Step Solution:

Solution :

Step 1 of 1:

The velocity in the top plate relative to the bottom plate V is

V=

Where is the shear stress applied to the top plate.

Here ,.

h is the thickness of the fluid layer.

Here , and

is the velocity of the fluid.

Here .

Our goal is :

We need to estimate V and the relative uncertainty in the estimate.

Now we need to estimate V and the relative uncertainty in the estimate.

First, we have to estimate the V value.

We know that and .

The estimate of V is

 

.

Therefore the estimate of V is 283.4899 mm/s.

Then the relative uncertainty in the logarithm of quantity is

Now computing the partial derivatives of .

Here we are differentiating with respect .

We know that  value.

Therefore .

Then,

Here we are differentiating with respect .

We know that h value.

 

Therefore .

Now we have to find the relative uncertainty in the estimate.

Then,

We substitute all the values in the above equation.

Therefore the relative uncertainty in the estimate is 0.025.

Hence .


Step 2 of 1

Chapter 3.4, Problem 21E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

The answer to “Refer to Exercise 10 in Section 3.2. Assume that ? = 35.2 ± 0.1 Pa, h = 12.0 ± 0.3 mm, and ? = 1.49 Pa · s with negligible uncertainty. Estimate V, and find the relative uncertainty in the estimate.Exercise 10: In a Couette flow, two large flat plates lie one on top of another, separated by a thin layer of fluid. If a shear stress is applied to the top plate, the viscosity of the fluid produces motion in the bottom plate as well. The velocity V in the top plate relative to the bottom plate is given by V = ?h/?, where ? is the shear stress applied to the top plate, h is the thickness of the fluid layer, and ? is the viscosity of the fluid. Assume that ? = 1.49 Pa • s and h = 10 mm, both with negligible uncertainty.a. Suppose that ? = 30.0 ± 0.1 Pa. Estimate V, and find the uncertainty in the estimate.b. If it is desired to estimate V with an uncertainty of 0.2 mm/s, what must be the uncertainty in ??” is broken down into a number of easy to follow steps, and 185 words. Since the solution to 21E from 3.4 chapter was answered, more than 286 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The full step-by-step solution to problem: 21E from chapter: 3.4 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This full solution covers the following key subjects: uncertainty, estimate, negligible, Find, exercise. This expansive textbook survival guide covers 153 chapters, and 2440 solutions.

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Refer to Exercise 10 in Section 3.2. Assume that ? = 35.2