The slope of the free surface of a steady wave in one-dimensional flow in a shallow liquid

Question:

The slope of the free surface of a steady wave in one-dimensional flow in a shallow liquid layer is described by the equation

\[\frac{\partial h}{\partial x}=-\frac{u}{g} \frac{\partial u}{\partial x}\]

Use a length scale, $L$, and a velocity scale, $V_{0}$, to nondimensionalize this equation. Obtain the dimensionless groups that characterize this flow.

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

Step by Step Answer:

Related Book For book-img-for-question

Fox And McDonald's Introduction To Fluid Mechanics

ISBN: 9781118912652

9th Edition

Authors: Philip J. Pritchard, John W. Mitchell

See More Books

Question Posted: May 06, 2024 08:00 AM

See More Questions

One-dimensional unsteady flow in a thin liquid layer is described by the equation \[\frac{\partial u}{\partial t}+u \frac{\partial u}{\partial x}=-g \frac{\partial h}{\partial x}\] Use a length...
An unsteady, two-dimensional, compressible, inviscid flow can be described by the equation \[\begin{aligned}\frac{\partial^{2} \psi}{\partial t^{2}}+\frac{\partial}{\partial t} & \left(u^{2}+v^{2}...
Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...
Which set of parametric equations is shown in the graph below? Explain your reasoning. (a) (b) x = t y = f
Find the equation of the plane containing the line x = 1 + 2t, y = -1 + 3t, z = 4 + t and the point (1, -1, 5).
Player I chooses a positive integer x > 0 and player II chooses a positive integer y > 0. The player with the lower number pays a dollar to the player with the higher number unless the higher number...
Which of the following suggestions is wrong? Mints set out a number of ways that auditor/auditee relations might be improved: a. Better understanding and communications by the auditor. b. Use a...
Identify the two recognized lease-accounting methods for lessees and distinguish between them.
Problem 1-01A a-b On April 1, Dorothy Taylor established Taylor's Travel Agency. The following transactions were completed during the month. 1. 2. 3. 4. 5. Invested $16,000 cash to start the agency....
In atmospheric studies the motion of the earth's atmosphere can sometimes be modeled with the equation \[\frac{D \vec{V}}{D t}+2 \vec{\Omega} \times \vec{V}=-\frac{1}{ho} abla p\] where $\vec{V}$...
Consider the flow field formed by combining a uniform flow in the positive $x$ direction and a source located at the origin. Obtain expressions for the stream function, velocity potential, and...
For an in-control process with subgroup data n = 3, = 100, and = 3.386, compute the percentage of outcomes within specifications if a. LSL = 98 and USL = 102. b. LSL = 93 and USL = 107.5. c. LSL =...
2. (10 pts each) Use partial fractions decomposition and the tables to find the inverse z- transform of each of the following: a. X(z)= 6z-z z3-4z2-z+4 4z2 b. G(z)=- (z-1) (z-0.5) 3z +1 c. X(z) =...
The following table contains the monthly operating costs of a company. Salary is not included. Determine the variance and standard deviation of the costs. Enero Febrero Marzo Abril Mayo Junio Julio...
Becker & Smith, CPAs, performs a financial statement review for BAM Markets ( BAM ) . Caroline, the manager on the job, learns that Don, a member of the review team, violated the independence rules....
Presented here are selected transactions for Sheridan Inc. during August of the current year. Sheridan uses a perpetual inventory system. It estimates a return rate of 10%, based on past experience....
. Complete both parts (a) and (b) below. ). In1 (a) Let X11, X12, ..., X be a random sample of size n from a population with mean and variance . Let X21, X22,..., X2n2 be a random sample of size n...
Gumball Candies manufactures jaw- breaker candies in a fully automated process. The company recently purchased a machine that can produce 4,500 candies per month. The machine costs $ 8,000 and is...
A statistical study shows that the fraction of television sets of a certain brand that are still in service after x years is given by f (x) = e-0.15x. (a) What fraction of the sets are still in...
Hoffman Corporation issued $95 million of 5%, 10-year bonds at 102. Each of the 95,000 bonds was issued with 12 detachable stock warrants, each of which entitled the bondholder to purchase, for $28,...
BACC460 Assignment 4 (LO3) Trial balance data for Peanut and Snoopy as of December 31, 2018 follows. Peanut company acquired 100% of the shares of Snnopy at $ (700,220) when the book value of Snoopys...
In 2016, Manhoff Company had a break-even point of $350,000 based on a selling price of $5 per unit and fixed costs of $112,000. In 2017, the selling price and the variable costs per unit did not...

The slope of the free surface of a steady wave in one-dimensional flow in a shallow liquid

Question:

Step by Step Answer:

Fox And McDonald's Introduction To Fluid Mechanics

Students also viewed these Engineering questions