Concept explainers
(a)
The axial speeds
Answer to Problem 65EP
The axial speed
The axial speed
Explanation of Solution
Given information:
The diameter at the entrance of the nozzle is
Write the expression for axial speeds at the nozzle entrance.
Here, the volume flow rate is
Write the expression for axial speeds at the nozzle exit.
Here, the axial speed at the exit of the nozzle is
Calculation:
Substitute
Substitute
Conclusion:
The axial speeds
The axial speeds
(b)
The several streamlines in the
Answer to Problem 65EP
The following figure represents the stream lines.
Explanation of Solution
Given information:
The diameter at the entrance of the nozzle is
Write the expression for axial speeds at the nozzle entrance.
Here, the volume flow rate is
Write the expression for axial speeds at the nozzle exit.
Here, the axial speed at the exit of the nozzle is
Write the expression for stream function of the flow filed.
Here, the stream function of the flow field is
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
The different values of stream function and radius are shown below the table.
| | | |
| | | |
| | | |
| | | |
| | | |
The following figure represents the stream line with varying of length.
Figure-(1)
For design, the shape of the nozzle is like the graph of the boundary layers.
Conclusion:
The following figure represents the stream lines.
Want to see more full solutions like this?
Chapter 9 Solutions
Fluid Mechanics: Fundamentals and Applications
- Consider a uniform stream of magnitude V inclined at angle ?. Assuming incompressible planar irrotational flow, find the velocity potential function and the stream function. Show all your work.arrow_forwardFluid Mechanics Question An incompressible fluid flows in the converged nozzle provided in the figure. nozzle area -> A=Ao*(1-b*x) entry speed -> V=Vo*(0.5+0.5*cos(w*t)) Vo:20m/s Ao=1.5 m2 L=13m b=0.2/22 W=0.16rad/s Find the acceleration in the nozzle center as a function of time * (to multiplication) / (to divide)arrow_forwardPlease help me in answering the following practice question. Thank you for your help. Consider several elementary planar irrotational flows arranged in a plane in a cartesian coordinate system (x-y plane) with the unit of length in m (meter). A line source with strength 18 m^2/s is located at point A (0, 1); a line sink with strength of 15 m^2/s is located at point B (3, -2); a line vortex with strength of 9 m^2/s is located at point C (4, 1); and a uniform flow of 10 m/s is at angle 30° with positive x-direction (counter-clockwise). Find the resultant velocity and pressure induced at point D (2, 0) by the uniform stream, line source, line sink & line vortex. Pressure at the infinity at upstream of uniform flow is 1000 Pa.Please list all necessary assumptions.arrow_forward
- A stirrer mixes liquid chemicals in a large tank. The free surface of the liquid is exposed to room air. Surface tension effects are negligible. Discuss the boundary conditions required to solve this problem. Specifically, what are the velocity boundary conditions in terms of cylindrical coordinates (r, ?, z) and velocity components (ur, u?, uz) at all surfaces, including the blades and the free surface? What pressure boundary conditions are appropriate for this flow field? Write mathematical equations for each boundary condition and discuss.arrow_forwardOuter pipe wall Consider the steady, incompressible, laminar flow of a Newtonian fluid in an infinitely long round pipe annulus of inner radius R, and outer radius Ro. Assume that the pressure is constant everywhere there is no forced pressure gradient driving the flow, Pi = P2. However, let the inner cylinder be moving at steady velocity V to the right, essentially a piston. The outer cylinder is stationary. This makes an axisymmetric Couette flow. Use cylindrical coordinates and the equations of motion to generate an expression for the x-component of velocity u as a function of r. Ignore the effects of gravity. Fluid: p, H iP R; R, ƏP_ P2- P1 ax x2-X1arrow_forwardHello sir Muttalibi is a step solution in detailing mathematics the same as an existing step solution EXAMPLE 6-1 Momentum-Flux Correction Factor for Laminar Pipe Flow CV Vavg Consider laminar flow through a very long straight section of round pipe. It is shown in Chap. 8 that the velocity profile through a cross-sectional area of the pipe is parabolic (Fig. 6-15), with the axial velocity component given by r4 V R V = 2V 1 avg R2 (1) where R is the radius of the inner wall of the pipe and Vavg is the average velocity. Calculate the momentum-flux correction factor through a cross sec- tion of the pipe for the case in which the pipe flow represents an outlet of the control volume, as sketched in Fig. 6-15. Assumptions 1 The flow is incompressible and steady. 2 The control volume slices through the pipe normal to the pipe axis, as sketched in Fig. 6-15. Analysis We substitute the given velocity profile for V in Eq. 6-24 and inte- grate, noting that dA, = 2ar dr, FIGURE 6–15 %3D Velocity…arrow_forward
- [4] Consider steady, incompressible, laminar flow of a Newtonian fluid in the narrow gap between two infinite parallel plates. The top plate is moving at speed V, and the bottom plate is stationary. The distance between these two plates is he, and the gravity acts in the negative z-direction (in to the page). There is no applied pressure other than hydrostatic pressure due to gravity. This flow is called Couette flow. Calculate the velocity and pressure fields, and estimate the shear force per unit area acting on the bottom plate. Moving plate Flui Finod platearrow_forwardQ1:- (a) Show that stream function exists as a consequence ofequation of continuity.(b) Show that potential function exists as a consequence ofirrotational flowarrow_forwardBriefly explain the purpose of the Reynolds transport theorem (RTT). Write the RTT for extensive property B as a “word equation,” explaining each term in your own words.arrow_forward
- A potential steady and incompressible air flow on x-y plane has velocity in y-direction v= - 6 xy . Determine the velocity in x-direction u=? and Stream Function SF=? ( x2 : square of x ; x3: third power of x ; y2: square of y , y3: third power of y)ANSWER: u= 3 x2 - 3 y2 SF= 3 x2 y - y3arrow_forwardFor a doublet of strength 20 m/s, calculate the velocity at point P(1, 2) and the value of stream function passing through it. [Ans. 0.636 m/s, -1.274 m2/s)arrow_forwardConsider inviscid flow along the streamline approachingthe front stagnation point of a sphere, as in Fig. Find(a) the maximum fluid deceleration along this streamlineand (b) its position.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning