Consider steady, incompressible, two-dimensional flow through a converging duct. Asimple approximate velocity field for this flow isV = (u, v) = (Uo + bæ)i – byjwhere UO is the horizontal speed at x = 0. Note that this equation ignores viscouseffects along the walls but is a reasonable approximation throughout the majority ofthe flow field. Find an analytical equation of streamline for this flow.

Answered: Image /qna-images/answer/fe50d116-73b2-433f-8169-6c73a3c7038f.jpg

Consider steady, incompressible, two-dimensional flow through a converging duct. A simple approximate velocity field for this flow is V = (u, v) = (U, + bx)i – byj O. Note that this equation ignores viscous where UO is the horizontal speed at x = effects along the walls but is a reasonable approximation throughout the majority of the flow field. Find an analytical equation of streamline for this flow.

Consider steady, incompressible, two-dimensional flow through a converging duct. A simple approximate velocity field for this flow is V = (u, v) = (U, + bx)i – byj O. Note that this equation ignores viscous where UO is the horizontal speed at x = effects along the walls but is a reasonable approximation throughout the majority of the flow field. Find an analytical equation of streamline for this flow.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

The velocity field for steady, incompressible, two-dimensional flow through a converging duct is: V=(Uo + bx)i -byj. Develop an analytical expression for the flow streamlines. Note that U0 and b are parameters and can be treated as constants.
The velocity distribution for turbulent flow in pipe is given approximately by Prandtl's one-seventh power law. u = UL where u is the local velocity of flow at a distance y from the pipe wall, Um is the maximum velocity at the centre line of the pipe and ro is the pipe radius. Find the following: (i) Average velocity, (ii) Kinetic energy correction factor, and (iii) Momentum correction factor
Consider the two-dimensional flow of an inviscid, incompressible fluid described by the superposition of a parallel flow of velocity V0, a source of strength q, and a sink of strength −q, separated by a distance b in the direction of the parallel flow, the source being upstream of the sink. (a) Find the resultant stream function and velocity potential. (b) Sketch the streamline pattern. (c) Find the location of the upstream stagnation point relative to the source.
The flow through a rectangular channel (width in x and height in z) is nonuniform with a velocity profile of V(z) = mz+b. The velocity at the floor of the channel is V(z=0) and the velocity at the top of the channel is V(z=Z). a) Develop an expression for flow rate and average velocity using the given constants. If the channel is 5m wide in x and 3m tall in z and V(z=0) = 0 m/s and V(z=3m) = 6 m/s: b) Determine the value of the constants m and b in the velocity profile c) Determine the value of the flowrate and average velocity of water in the channel.
A fluid of constant density flows at the rate of 15 li/sec along a pipe AB of 100-mm-diameter. This pipe branches at B into two pipes BC and BD each of 25 mm diameter and a third pipe BE of 50 mm diameter. The flow rates are such that the flow through BC is three times the flow rate through BE and the velocity through BD is 4 m/sec. Find the flow rates (m^3/s) in the three branches (a) BC, (b) BD and (c) BE. ,
Which of the following is a valid potential function for incompressible flow? (Assume A is numerical constant). A B C D None of these o = Alog₂ xy ¢ = A(cosx + sin!) =(x²-y²)
(a) The velocity vector in an incompressive flow is given by V = (6xt + yz² )i + (3t+ xy² )j + (xy − 2xyz – 6tz) k - - (i) Verify whether the continuity equation is satisfied.
In using Darcy-Weisbach equation for flow in a pipe, the friction factor is misjudged by + 25%. The resulting error in the estimated discharge Q is
Does the function, =Ur cose+cose represent possible irrotational flow? r
PROBLEM 04: The fluid in the figure is water, with the surface 20m above the datum. The pipe is 15cm in diameter and the head losses are as follows: from 1 to 2, 0m; from 2 to 3, 0.60m; from 3 to 4, 2m; and from 4 to 5, 0.30m. a) Determine the velocity of flow in the pipe in m/s. b) Determine the discharge Q in m^3/s. c) How many meters above the center of the pipe will water stand in piezometer tube 3? d) How many meters above the center of the pipe will water stand in piezometer tube 4?
At two points 1 and 2 in a pipeline the velocities are V and 2V, respectively. Both the points are at the same elevation. The fluid density is p. The flow can be assumed to be incompressible, inviscid, steady and irrotational. The difference in pressures P₁ and P₂ at 1 2 points I and 2 is
Given the pipe system and velocities (m/s) shown. A₁ = 0.1 m² A₂ = 0.15 m² A3 = 0.2 m² 1 V₁ = 10 e-t/2 3 ↑ V3 = 2 сos(2лt) a. Find an expression for V2. b. Find the initial time that V₂ first is zero. c. Find the mean volumetric flow at 2. 2 V₂ = ?