Consider the fully-developed steady-state laminar flow of a Newtonian fluid in a vertical pipe of radius...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Consider the fully-developed steady-state laminar flow of a Newtonian fluid in a vertical pipe of radius R which is rotated at the constant angular velocity , and also is subject to an axial pressure gradient and gravity forces in the negative z-direction. a) Determine the relative forms of the continuity and momentum equations. b) Write the boundary conditions on the equations in part (a). c) Solve the above to obtain the velocity profile for the circumferential velocity. d) Determine the pressure profile P(r,z). e) Determine the axial velocity profile. f) Scale these differential equations to determine under what conditions the pressure forces can be neglected relative to the gravity forces. Express your answer in terms of dimensionless group which must be very large or very small in order to neglect the pressure forces. g Consider the fully-developed steady-state laminar flow of a Newtonian fluid in a vertical pipe of radius R which is rotated at the constant angular velocity , and also is subject to an axial pressure gradient and gravity forces in the negative z-direction. a) Determine the relative forms of the continuity and momentum equations. b) Write the boundary conditions on the equations in part (a). c) Solve the above to obtain the velocity profile for the circumferential velocity. d) Determine the pressure profile P(r,z). e) Determine the axial velocity profile. f) Scale these differential equations to determine under what conditions the pressure forces can be neglected relative to the gravity forces. Express your answer in terms of dimensionless group which must be very large or very small in order to neglect the pressure forces. g
Expert Answer:
Answer rating: 100% (QA)
Question a The relative forms of the continuity and momentum equations are as follows Continuity equ... View the full answer
Related Book For
Fundamentals of Thermal-Fluid Sciences
ISBN: 978-0078027680
5th edition
Authors: Yunus A. Cengel, Robert H. Turner, John M. Cimbala
Posted Date:
Students also viewed these physics questions
-
Consider laminar flow of a Newtonian fluid of viscosity μ between two parallel plates. The flow is one-dimensional, and the velocity profile is given as u(y) = 4u max [y/h - (y/h) 2 ],...
-
A rod subject to an axial load (Figure) will be deformed, as shown in the stress-Strain curve in Figure. The area under the curve from zero stress out to the point of rupture is called the modulus of...
-
A Newtonian fluid in continuous, in-compressible laminar flow is moving steadily through a very long 700-m, horizontal pipe. The inside radius is 0.25 m for the entire length, and the pressure drop...
-
A horizontal cross section of a concrete bridge pier is a regular hexagon (six sides, all equal in length, and all internal angles are equal), each side of which is 2.50 m long. If the height of the...
-
Using data in Appendix C, calculate ÎH°, ÎS°, and ÎG° at 298 K for each of the following reactions. In each case show that ÎG° = ÎH° -...
-
A system consists of three identical 19.32-lb particles A, B, and C. The velocities of the particles are, respectively, vA = vA j, vB = vB i, and vC = vCk, and the magnitude of the linear momentum L...
-
What roles do code review and testing play in quality assurance? Compare and contrast.
-
The balance sheet of Kishwaukee Corporation as of December 31, 2014, is as follows. Note 1: Buildings are stated at cost, except for one building that was recorded at appraised value. The excess of...
-
Image transcription text Directional Behavior VCL Transcript This week, we've introduced the idea of directional behavior of materials. We're about ready to explore that a little bit more using the...
-
Determine the monthly cash flows and total cash generated at the end of each month and just before the payment is received for the construction of a house with the following budget and schedule. On...
-
Louisa is the delivery manager at a luggage manufacturing company. She must inform her supervisor that the shipment of a particular batch of luggage will be delayed because a team member made a...
-
A mass m = : 22.3kg is supported against gravity by three ropes. Rope 1 pulls directly to the right (in the positive x-direction) exerting a force of magnitude T = 38.3N. Rope 2 pulls up and to the...
-
On Earth you weigh 6 0 0 N . On another planet your weight ( the gravity force from the planet exerts on you ) is 4 0 0 N . If the mass of the planet is 4 . 0 0 * 1 0 2 4 kg , , what is its radius?
-
Three clowns move a 295 kg crate 12.0 m to the right across a smooth floor. Take the positive horizontal and vertical directions to be right and up, respectively. Moe pushes to the right with a force...
-
A fully loaded diesel engine operating at sea level runs at 2000 rpm and develops 1000 bhp (750 kW). The initial operating temperature of the engine is 518.7R (288.15K). Metered fuel injection is...
-
A patient is being admitted to receive a high-cost medication at a dose of 1000 mg/hr for 48 hours. The medication is only available in 6-gram vials. In order to minimize waste, what is the lowest...
-
Buildings $ 27,500 Accounts receivable 2,100 Land 16,200 Merchandise inventory 7,200 Accounts payable 5,100 Cash 8,200 Notes payable (due in 7 years) 32,000 Office supplies 1,200 Common stock 7,000...
-
(a) What is the focal length of a magnifying glass that gives an angular magnification of 8.0 when the image is at infinity? (b) How far must the object be from the lens?
-
Two parallel disks of diameter D = 0.6 m separated by L = 0.4 m are located directly on top of each other. Both disks are black and are maintained at a temperature of 450 K. The back sides of the...
-
A 2.4-in-diameter soap bubble is to be enlarged by blowing air into it. Taking the surface tension of soap solution to be 0.0027 lbf/ft, determine the work input required to inflate the bubble to a...
-
Define pressure head, velocity head, and elevation head for a fluid stream and express them for a fluid stream whose pressure is P, velocity is V, and elevation is z.
-
Sketch and explain a simple diagram to match your exhibit.
-
a. Write out and explain the equation for volume breakeven. b. What is the difference between accounting breakeven and economic breakeven?
-
a. What is profit analysis, also known as cost-volume-profit (CVP) analysis? b. Why is profit analysis so useful to healthcare managers? c. What is a profit and loss (P&L) statement?
Study smarter with the SolutionInn App