Consider steady, incompressible, laminar flow of a Newtonian fluid in an infinitely long round pipe of diameter D or radius R = D/2 inclined at angle a. There is no applied pressure gradient (@P/x = 0). Instead, the fluid flows down the pipe due to gravity alone. We adopt the coordinate system shown, with x down the axis of the pipe. Derive an expression for the x- component of velocity u as a function of radius r and the other parameters of the problem. Calculate the volume flow rate and average axial velocity through the pipe. 102 α Pipe wall Fluid: p. R X

Consider steady, incompressible, laminar flow of a Newtonian fluid in an infinitely long round pipe of diameter D or radius R = D/2 inclined at angle a. There is no applied pressure gradient (@P/x = 0). Instead, the fluid flows down the pipe due to gravity alone. We adopt the coordinate system shown, with x down the axis of the pipe. Derive an expression for the x- component of velocity u as a function of radius r and the other parameters of the problem. Calculate the volume flow rate and average axial velocity through the pipe. 102 α Pipe wall Fluid: p. R X

Name: Consider steady, incompressible, laminar flow of a Newtonian fluid in
Uploaded: 2024-03-20T06:56:55.000Z
Channel: Bartleby
Description: Consider steady, incompressible, laminar flow of a Newtonian fluid in aninfinitely long round pipe of diameter D or radius R = D/2 inclined at anglea. There is no applied pressure gradient (@P/x = 0). Instead, the fluidflows down the pipe due to gra

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

find:v Maximum speed Average speed Volumetric flow Show that the speed profile provided satisfies the continuity equation in its differential format Incompressible steady flow in the inlet between parallel plates is uniform, Vo = 8 cm/s, while downstream, the flow develops into the parabolic profile = az(zo-z), where a is a x constant. What is the maximum value of v,? Vo
Problem 3. A two dimensional ensional velocity field is 5 = 7xyî - by² Ĵ 2 R (a) Determine the fluid acceleration at x-4, y-5. (b) Determine the rate of volumetric dilatation in the flow. If we assume that this flow is incompro the conservation of incompressible, does this satisfy mass (show your calculations to justify the answer)? angular rotation a fluid element. (c) Determine the rate of of (W = 1/2 √ × 8 ) given by:
In an experiment to determine the force acting on an oval-shaped body, a model is mounted in the test section of a wind tunnel. The test section itself has rectangular cross section with height 2h and width l (into the page). The model spans the entire width of the test section. The model is subject to a steady, uniform, incompressible flow of velocity V₁. The pressure gauge indicates a pressure difference (Ap) between the test section exit (location 2) and the test section entrance (location 1). The velocity profile downstream of the model is shown in the figure. Use the control volume shown. Find the force acting on the model in terms of given quantities V₁, h, l, Ap, and density, p. Ap V AL
Need help on both parts please
Given the vector equation below for velocity of a given fluid: V=(0.5+1.2x)i + (-2.0-1.2y)j, derive an analytical expression for the flow streamlines
Need Solution through 15min
6. For a two-dimensional flow, the velocity field is ū = 1²+y • jwhere i and j are the basis vectors in the x-y Cartesian coordinate system. Identify the CORRECT statements from below. (1) The flow is incompressible. (2) The flow is unsteady. -y (3) y-component of acceleration, ay (z²+y²)² -(z+y) (4) x-component of acceleration,az (2²+y?)² (A) (2) and (3) (B) (1) and (3) (C) (1) and (2) (D) (3) and (4)
4. Fluid flows axially in the annular space between a cylinder and a concentric rod. The radius of the rod is r; and that of the cylinder is ro. Fluid motion in the annular space is driven by an axial pressure gradient dp/dz. The cylinder is maintained at uniform temperature To. Assume incompressible laminar axisymmetric flow and neglect gravity and end effects. Show that the axial velocity is given by: _1-(r; /r, )? In(r, / r; ) r dp |(r/r,)? Au dz - In(r / r, ) – 1
6)
Please answer both
The velocity distribution in a 0.02 m diameter horizontal pipe conveying carbon tetrachloride (specific gravity = 1.59, absolute viscosity = 9.6 x 10-6 Pa sec) is given by the parabolic equation: v(r)=0.01(0.12- r?), where v(r) is the velocity in (m/s) at a distance r in (m) from the pipe center. What is discharge? O a. 3.13 x-8 m3/s O b. None of the mentioned O c. 1.047 x 108 m3/sec O d. 4.97 x 109 m3/sec
P1 A thin layer of water flows down a plate inclined to the horizontal with an angle a = 15° in the shown coordinate system. If the thickness of the water layer is a=0.5 mm, assuming that the flow is laminar and incompressible, (water density p = 1000 kg/m³viscosity µ = 0.001 Pa.s and acceleration of gravity g = 9.81 m/s²) and an air flow shears the layer in a direction opposite to its flow with a shear stress of 1 N /m². Solve the Navier-Stokes equation: air water (a) to find the value of the maximum water velocity in m/s to three decimal points, Answer: (b)and to find the value of water velocity at the layer's surface in m/s to three decimal points, Answer: