(a)
The characteristic scale for v, y-component of velocity.
Answer to Problem 27P
The characteristic scale for v, y-component of velocity is
Explanation of Solution
First, we need to use continuity equation for velocity component.
From continuity equation,
We have,
Now, to obtain order of magnitude. We need to use characteristic scale separately.
We have,
Now, characteristic scale v is,
(b)
The order of magnitude of inertial term to that of viscous and pressure term.
Answer to Problem 27P
The characteristic scale for v, y-component of velocity is
Explanation of Solution
First, we need to use momentum of x-component.
As we know that the flow is carried out in two-dimensional, so the z component will be zero.
Now, to obtain order of magnitude. We need to use characteristic scale separately.
We have,
Now,
The second term of viscosity is very smaller as compared to the second viscous term. So, we neglect this term (ho<
Now, we need to multiply all the order of magnitude with a factor of
Now,
We can see that the order of magnitude consists a factor of
(c)
If the value of Reynolds number is less than 1 and (ho<
Explanation of Solution
First, we need to use momentum of x-component.
As we know that the flow is carried out in two-dimensional, so the z component will be zero.
Now, to obtain order of magnitude. We need to use characteristic scale separately.
We have,
Now,
The second term of viscosity is very smaller as compared to the second viscous term. So, we neglect this term. (ho<
Now,
We can see that the order of magnitude consists a factor of
Want to see more full solutions like this?
Chapter 10 Solutions
Fluid Mechanics: Fundamentals and Applications
- find mach and reynolds number and write out N-S eqnsarrow_forwardPlease answer with detailarrow_forward1. The Stokes-Oseen formula for drag force Fon a sphere of diameter D in a fluid stream of low velocity V, density p, and viscosity u is: 9T F = 3TuDV + 16PD? Is this formula dimensionally homogenous? 2. The efficiency n of a pump is defined as the (dimensionless) ratio of the power required to drive a pump: QAp input power Where Q is the volume rate of flow and Ap is the pressure rise produced by the pump. Suppose that a certain pump develops a pressure of Ibf/in? (1ft = 12 in) when its flow rate is 40 L/s (1L =0.001 m). If the input power is 16hp (1hp = 760 W), what is the efficiency?arrow_forward
- The x-component of the Navier-Stokes equations is given below. Convert it to dimensionless form using a velocity scale U, a length scale I, and a pressure scale P. du at du du du +u+v+w. = ax dy az 1 op μdu du du + + pax² ay ² a=² paxarrow_forwardAy j. Is this a possible case of incompres- 3.9 A velocity field is given by V= Axyi -- %3D sible flow? If yes, obtain the stream function and find the value of constant A for which the flow rate between the streamlines passing through the points (3, 3) and (3, 4) is 18 units. Axy Ans: V = 12 + C, A 7 2arrow_forwardFind the vorticity of the fluid motion for the given velocity com- ponents. KINEMATICS OF FLUIDS (a) u A(x + y), v = - A(x + y) (b) u = 2Axz, (c) u Ay²+ By + C, v = A(c² + x² - z²) 1)=0arrow_forward
- FLUID MECHANICSarrow_forwardTwo infinite plates a distance h apart are parallel to the xzplane with the upper plate moving at speed V, as inFig. There is a fluid of viscosity μ and constant pressurebetween the plates. Neglecting gravity and assumingincompressible turbulent flow u(y) between the plates, usethe logarithmic law and appropriate boundary conditions toderive a formula for dimensionless wall shear stress versusdimensionless plate velocity. Sketch a typical shape of theprofile u(y).arrow_forwardConsider a two-dimensional flow in the upper half plane of (x, y) bounded below by a Fid plate coinciding with the x axis. At t= 0 the plate suddenly moves in the tangential direction at constant velocity 'U'. The velocity distribution of the flow is y erf(- 2vt obtained as u=U|1- Using the properties of the error function i) verify whether u is satisfying the conditions: (a) u=U at y=0_(for t20) (b) u=0 as y→0 (for t>0) (for V y) (c) u=0 at t=0 du ii) determine the stress at wall using the condition T (0,1)=µ dy ly-0 Once you upload files from your second device, click on C Sync to check your submission Cameraarrow_forward
- PLS SHOW ME FULL STEPS SIR PLS ANSWER WITHIN 30 MIN SIR SUBJECT (FLUID MECH 2) use setting 2arrow_forwardIn deriving the vorticity equation, we have used the identity divergence x (divergence P) = 0 Show that this identity is valid for any scalar lamda by checking it in Cartesian and cylindrical coordinates.arrow_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
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY