Concept explainers
The expression for stream function.
The plot some streamlines of the flow.
Answer to Problem 63EP
The expression for the stream function is
The following figure represents the streamlines of the flow.
Explanation of Solution
Given information:
The incompressible flow filed for which the velocity
Write the expression for the velocity along
Here, the stream function along
Write the expression for the velocity along
Here, the stream function along
Write the expression for quadric stream function.
Here, the stream function is
Calculation:
Substitute
Integrate Equation (IV) with respect to
Here, the constant is
Substitute
Differentiate Equation (V) with respect to
Substitute
Substitute
Here, the constant is
Substitute
Substitute
Substitute
Substitute
Solve Equation (XII) by taking positive sign.
Solve Equation (XII) by taking negative sign.
The following table shows that the value of stream function with respect to value of
| | | |
| | | |
| | | |
| | | |
Plot the streamlines on y x plane by using Equation (XII) and the range of
Figure-
The Figure
Conclusion:
The expression for the stream function is
The following figure represents the streamlines of the flow.
Want to see more full solutions like this?
Chapter 9 Solutions
Connect Access for Fluid Mechanics
- Consider a 2-dimensional incompressible flow field. The vertical component of velocity forthe flow field is given by 2y. The pressure at (x, y) = 0,0 is given by 3 bar absolute. The densityof the fluid is 1.2 Kg/m3 . Find. a) x-component of velocity; b) acceleration at point (x, y) = 2,1;c) pressure gradient at the same point; d) pressure gradient along the x-axis; e) check whetherthe flow is irrotational; f) find the potential function; g) find the stream function; h) equationfor streamline and sketch few streamlines.arrow_forwardConsider a velocity field where the x and y components of velocity aregiven by u = cy/(x2 + y2) and v = −cx/(x2 + y2), where c is a constant.Obtain the equations of the streamlines.arrow_forwardThe expression for stream function is described by y = x ^ 3 - 3x * y ^ 2 . Indicate whether the flow is rotational or irrotational. Determine the value or velocity potential o, if it exists.arrow_forward
- Determine whether each of the followings are rotational flow or irrotational flow. Also, determine their stream functions. (u: x-component of velocity. v: y-component of velocity.) 1. u=x^3-3(x)(y^2), v=y^3-3(x^2)(y) 2. u=2xy, v=-y^2arrow_forwardConsider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and v = 2yt. Do the fluid elements experience angular rotation? Thus, state whether the flow field is rotational or irrotational.arrow_forwardA velocity field is given by V= xi+ x(x-1)(y+ 1)j, where x and y are in feet. Plot the stream line that passes through, x= y= 0 for the range, -1 ≤ x≤ 3 and -0.5 ≤ y≤ 3.5arrow_forward
- Find the stagnation point in the following two-dimensional velocity field: V=(3+x-y)i + (5+x+y)jarrow_forward1. Find the velocity at a point (4, 3, 1) after 2 sec. for a three dimensional flow given by Eq.1. ? 2. Determine whether the continuity equation is satisfied? 3. Show that this flow is kinematically possible? 4. Is the fluid flow irrotational?arrow_forwardVelocity components in the flow of an ideal fluid in a horizontal plane; Given as u = 16 y - 12 x , v = 12 y - 9 x a) Is the current continuous?(YES OR NO) b) Can the potential function be defined?(YES OR NO) c) Find the unit width flow passing between the origin and the point A(2,4). (y(0,0)=0) d) Calculate the pressure difference between the origin and the point B(3;3).arrow_forward
- If the stream function is y = 2xy, then the velocity at a point (1, 2) is equal to:arrow_forwardConsider the velocity field given by u = y/(x2 + y2) and v = −x/(x2 + y2). Calculate the vorticity.arrow_forwardWhat are unique physical characteristics of the rotational flow in contrast to the irrotational flow?Determine whether the flow is rotational or irrotational using an expression for the vorticity of the flow field described by V = x2y i + xy2 j. (Please type answer no write by hend)arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning