In an irrotational region of flow, we write the velocity vector as the gradient of the scalar

Question:

In an irrotational region of flow, we write the velocity vector as the gradient of the scalar velocity potential function,

V(vector) in cylindrical coordinates, (r, u, z) and (u_r, u_θ, u_z), are

From Chap. 9, we also write the components of the vorticity vector in cylindrical coordinates as

Substitute the velocity components into the vorticity components to show that all three components of the vorticity vector are indeed zero in an irrotational region of flow.

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

Step by Step Answer:

Related Book For book-img-for-question

Fluid Mechanics Fundamentals And Applications

ISBN: 9780073380322

3rd Edition

Authors: Yunus Cengel, John Cimbala

See More Books

Question Posted: Sep 17, 2023 12:44 AM

See More Questions

Substitute the components of the velocity vector given in Prob. 1066 into the Laplace equation in cylindrical coordinates. Showing all your algebra, verify that the Laplace equation is valid in an...
In an irrotational region of flow, the velocity field can be calculated without need of the momentum equation by solving the Laplace equation for velocity potential function and then solving for the...
Consider a planar irrotational region of flow in the r-plane. Show that stream function satisfies the Laplace equation in cylindrical coordinates.
Presented here are summarized data from the balance sheets and income statements of Wiper Inc.: WIPER INC. Condensed Balance Sheets December 31, 2020, 2019, 2018 (in millions) 2020 2019 Current...
The continuously compounded annual return on a stock is normally distributed with a mean of 20% and standard deviation of 30%. With 95.44% confidence, we should expect its actual return in any...
Why do you think managers would want to use the balanced scorecard to measure and control organizational performance? LO.1
An increase in earnings _________ the P/E ratio.
Prepare journal entries to record the following merchandising transactions of Cabela's, which uses the perpetual inventory system and the gross method. July 1 Purchased merchandise from Boden Company...
Fill in the blanks in the following separate income statements a through e
The Sock Company buys hiking socks for $6 a pair and sells then for $10. Management budgets monthly fixed costs to be $12,000 per month. Required (consider each of the following questions...
Consider an irrotational line vortex of strength in the xy-or r-plane. The velocity components are Generate expressions for the velocity potential function and the stream function for the line...
Consider the following steady, two-dimensional, incompressible velocity field: Is this flow field irrotational? If so, generate an expression for the velocity potential function. V = (u, v) = (ay +...
In Problems 4958, determine whether the given set is finite or infinite. Consider the set N of positive integers to be the universal set, and let E P H = {ne N T = {ne N E = {ne N P = {n e N n >...
Given forecast errors of 4, 8, and -3, what is the MAD? What is the MSE?
Padgett Rentals can purchase a van that costs $$48,000$ ; it has an expected useful life of three years and no salvage value. Padgett uses straight-line depreciation. Expected revenue is...
Rainwater Corp. expects to sell 600 umbrellas in May and 400 in June. Each umbrella sells for $$15$. Rainwaters beginning and ending finished goods inventories for May are 75 and 50 units,...
Don Moon is the owner of ABC Cleaning. At the beginning of the year, Moon had $\$ 2,400$ in inventory. During the year, Moon purchased inventory that cost $\$ 13,000$. At the end of the year,...
Agua Ole is a distributor of bottled water. For each of items a through c, compute the amount of cash receipts or payments Agua Ol will budget for September. The solution to one item may depend on...
Grichuk Power leased high-tech electronic equipment from Kolten Leasing on January 1, 2018. Kolten purchased the equipment from Wong Machines at a cost of $112,080. Related Information: Lease term...
A researcher reports a significant two-way between-subjects ANOVA, F(3, 40) = 2.96. State the decision to retain or reject the null hypothesis for this test.
If two resistors R 1 and R 2 (R 2 > R 1 ) are connected in parallel as shown in Fig. Q26.6, which of the following must be true? In each case justify your answer. (a) I 1 = I 2 . (b) I 3 = I 4 . (c)...
A battery with no internal resistance is connected across identical light bulbs as shown in Fig. Q26.7. When you close the switch S, will the brightness of bulbs B 1 and B 2 change? If so, how will...
For the circuit shown in Fig. E26.7 find the reading of the idealized ammeter if the battery has an internal resistance of 3.26 Î©. Figure E26.7 45.0 0 25.0 V 18.0 N -w 15.0 N
Suppose I have computed the cost of carbon per mile for my car at 0 . 0 1 2 per mile. Assume that the interest rate is 4 % and that I drive the car 2 8 , 0 0 0 miles per year. What is the present...
Imagine that in stable growth period, the firm earns ROIC of 10% and has after tax EBIT of 200 and reinvestment $ of 40. What is the steady state growth rate? 20% O 10% 2%
Tanner-UNF Corporation acquired as a long-term investment $160 million of 5.0% bonds, dated July 1, on July 1, 2021. Company management has the positive intent and ability to hold the bonds until...

In an irrotational region of flow, we write the velocity vector as the gradient of the scalar

Question:

V = Vo.

Step by Step Answer:

In an irrotational region of flow the velocity vector is Now the components of in cylindric...View the full answer

Fluid Mechanics Fundamentals And Applications

Students also viewed these Engineering questions