Show that the unit vectors e r and e in a cylindrical coordinate system are related

Question:

Show that the unit vectors e_r and e_θ in a cylindrical coordinate system are related to the unit vectors e_x and e_y by

e_r = e_x cos θ + e_y sin θ

and

e_θ = -e_x sin θ + e_y cos θ

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Fundamentals Of Momentum Heat And Mass Transfer

ISBN: 9781118947463

6th Edition

Authors: James Welty, Gregory L. Rorrer, David G. Foster

See More Books

Question Posted: Oct 31, 2018 07:11 AM

See More Questions

Using the results of Problem 1.7, show that de r /d = e and de /d = -e r . Data From Problem 1.7 Show that the unit vectors e r and e in a cylindrical coordinate system are related to the unit...
Transform the operator to cylindrical coordinates (r, Î¸, z), using the results of Problems 1.7 and 1.9. Data From Problem 1.7 Show that the unit vectors e r and e Î¸ in a...
Find Dv/Dt in polar coordinates by taking the derivative of the velocity. (v = v r (r, , t)e r + v (r, , t)e . Remember that the unit vectors have derivatives.)
Modify your Digraph class from the previous exercise to make a MultiDigraph class that allows parallel edges. For a test client, run a random- surfer simulation that matches RandomSurfer (Program...
An airplane pilot fell 370 m after jumping from an aircraft without his parachute opening. He landed in a snow bank, creating a crater 1.1 m deep, but survived with only minor injuries. Assuming the...
10. value 2.00 points < Question 10 (of 10) Save & You find the following corporate bond quotes. To calculate the number of years until maturity, assume that it is currently January 15, 2016. The...
State casket sales restrictions. Some states permit only licensed firms to sell funeral goods (e.g., caskets, urns) to the consumer, while other states have no restrictions. States with casket sales...
1. What forms of homeowners insurance are available? Which forms should the Salazars consider? 2. What are the perils against which the home and its contents should be insured? 3. Discuss the types...
A company is considering an iron ore extraction project that requires an initial Investment of $520,000 and will yield annual cash inficiws of 152,000 for four years The company's discount rate is...
The Gidget Company makes widgets. If the production process is working properly, it turns out that the widgets are normally distributed with a mean length of at least 3.43.4 feet. Larger widgets can...
Using the information given in Problem 1.1 and the properties of the standard atmosphere given in Appendix G, estimate the number of molecules per cubic inch at an altitude of 250,000 ft. Data From...
Using the geometric relations given below and the chain rule for differentiation, show that and when r 2 = x 2 + y 2 and tanÎ¸ = y/x. sin 0 + cos 0. r r 0 cos 0 a r 0 + sin 0 r ||
The following information has been obtained for the Kerdyk Corporation. 1. Prior to 2007, taxable income and pretax financial income were identical. 2. Pretax financial income is $1,700,000 in 2007...
In the circuit shown below, IE = 120 mA, a = 0.99, a2 = 0.98. Assuming that both transistors are in the active state, answer the following questions: 1. Find IC, IB, IE, IC, and Ic. 2. Find the...
Find the open intervals where the function is concave upward or concave downward. Find any inflection points. f(x)=-(x+1)6 Find any critical numbers for f and then use the second derivative test to...
Worked Example A two-dimensional incompressible flow is expressed by the velocity functions: u = -2xy y = y = x 1 w=0 Find the pressure field p(x, y) when the pressure at the origin (x=o, y=o) is p.....
The following information is available for Blue Spruce Corp. for 2022. Cash used to purchase treasury stock Cash dividends paid $111,592 50,576 Cash paid for interest Net income 51,968 1,077,176...
3 4pts Foam k MA C L H W F A box is transported by a truck. Suddenly, the driver uses the brakes and applies 100 N deceleration force to the box. The weight of the box is 20 Kg and its dimensions are...
Is it possible that the points (2, 3), (5,1), and (1, 3) are all on the graph of the same function? Explain.
Conduct a VRIO analysis by ranking Husson University (in Maine) business school in terms of the following six dimensions relative to the top three rival schools. If you were the dean with a limited...
Steel (AISI 1010) plates of thickness = 6 mm and length L = 1 m on a side are conveyed from a heat treatment process and are concurrently cooled by atmospheric air of velocity u = 10 m/s and T =...
Steel (AISI 1010) plates of thickness = 6 mm and length L = 1 m on a side are conveyed from a heat treatment process and are concurrently cooled by atmospheric air of velocity u = 10 m/s and T =...
Tissue engineering involves the development of biological substitutes that restore or improve tissue function, Once manufactured, engineered organs can be implanted and grow within the patient,...
You plan to buy a house for $325,000 today. If the house is expected to appreciate in value 8% each year, what will its value be seven years from now?
A designated beneficiary of an ABLE account must be ___________ in order to meet the special rules that apply to the increased contribution limit authorized under the Tax Cuts and Jobs Act? a. an...
Stans wholesale buys canned tomatoes from canneries and sells them to retail markets Stan uses the perpetual inventory

Show that the unit vectors e r and e in a cylindrical coordinate system are related

Question:

Step by Step Answer:

QED erlerx exl...View the full answer

Fundamentals Of Momentum Heat And Mass Transfer

Students also viewed these Physics questions