Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 15, Problem 44CP
For each statement, choose whether the statement is e or false. and discuss your answer brieflv
(a) The physical validity of a CFD solution always improves as the grid is refined.
(b) The x-component of the Navier-Stokes equation is an example of a transport equation.
(c) For the same number of nodes m a two-dimensional mesh, a structured grid typically has fewer cells than an unstructured triangular
(d) A time-averaged turbulent flow CFD solution is only as good as the turbulence model used in the calculations.
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For each statement, choose whether the statement is true or false, and discuss your answer briefly: (a) The physical validity of a CFD solution always improves as the grid is refined. (b) The x-component of the Navier–Stokes equation is an example of a transport equation. (c) For the same number of nodes in a two-dimensional mesh, a structured grid typically has fewer cells than an unstructured triangular grid. (d ) A time-averaged turbulent flow CFD solution is only as good as the turbulence model used in the calculations.
Consider the 2-D incompressible, invisicid Navier-Stokes equation in the horizontal plane. Recall that the momentum equations are simply solving the transport of the velocity on a frozen velocity field. Use a finite volume method on a structured grid numbered i, j with uniform h = 0.3 in x and y, as shown in Fig. 4. Use typical numbering, e.g. ui,j refers to the solution for the i-th point in the x-, and j-th point in the y-direction. The fluid has a density of 1000 kgm3. Use first-order upwinding for the fluxes.The pressure field of the initial solution is taken as uniform pi,j = 0.Assume that you have computed the first step of the SIMPLE scheme from an initial solution, and the resulting velocity field u* is given by the components u = [u, v] ^T with u1,j = 1.1, u2,j= 1.5, u3,j = 2.5for all j except cell 2, 2, and ui,1 = 0.3, ui,2 = 0.5, ui,3 = 0.8 for all i except cell 2, 2. In cell 2,2 the velocity is u2,2 = [2, 0.6]^T.
a) Simplify the equations for the x− and y-momentum for this…
An underwater device which is 2m long is to be moved at 4 m/sec. If a geometrically
similar model 40 cm long is tested in a variable pressure wind tunnel at a speed of 60
m/sec with the following information,
Poir at Standard atmospheric pressure = 1.18kg/m³
Pwater = 998kg/m3
Hair = 1.80 x 10-5 Pa-s at local atmospheric pressure and
Hwater = 1 × 10-3 Pa-s then the pressure of the air in the model used
times local atmospheric pressure
is
Chapter 15 Solutions
Fluid Mechanics: Fundamentals and Applications
Ch. 15 - A CFD code is used to solve a two-dimensional (x...Ch. 15 - Write a brief (a few sentences) definition and...Ch. 15 - What is the difference between a node and an...Ch. 15 - Prob. 4CPCh. 15 - Prob. 5CPCh. 15 - Prob. 6CPCh. 15 - Prob. 7CPCh. 15 - Write a brief (a few sentences) discussion about...Ch. 15 - Prob. 9CPCh. 15 - Prob. 10CP
Ch. 15 - Prob. 11CPCh. 15 - Prob. 13CPCh. 15 - Prob. 14CPCh. 15 - Prob. 15CPCh. 15 - Prob. 16PCh. 15 - Prob. 17PCh. 15 - Prob. 18PCh. 15 - Prob. 19PCh. 15 - Prob. 20PCh. 15 - Prob. 21PCh. 15 - Prob. 22PCh. 15 - Prob. 23PCh. 15 - Prob. 24PCh. 15 - Prob. 25PCh. 15 - Prob. 26PCh. 15 - Prob. 27PCh. 15 - For each statement, choose whether the statement...Ch. 15 - Prob. 45CPCh. 15 - Gerry creates the computational domain sketched in...Ch. 15 - Think about modem high-speed, large-memory...Ch. 15 - What is the difference between mulugridding and...Ch. 15 - Suppose you have a fair) comp1c geometry and a CFD...Ch. 15 - Generate a computational domain and grid, and...
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- Consider the 2-D incompressible, invisicid Navier-Stokes equation in the horizontal plane. Recall that the momentum equations are simply solving the transport of the velocity on a frozen velocity field. Use a finite volume method on a structured grid numbered i, j with uniform h 0.3 in x and y, as shown in Fig. 4. Use typical numbering, e.g. ui, refers to the solution for the i-th point in the x-, and j-th point in the y-direction. = i- 1,j+1 i,j+1 i-1,j i-1,j-1 X i,j i+1, j+1 i+1,j i,j-1 i+1,j-1 Figure 4: Two-dimensional grid with equal spacing. The fluid has a density of 1000 kg. Use first-order upwinding for the fluxes. The pressure field of the initial solution is taken as uniform pij = 0. Assume that you have computed the first step of the SIMPLE scheme from an initial solution, and the resulting velocity field u* is given by the components u = [u, v]T with u₁.j = 1.1, U2,j 1.5, U3,j = 2.5 for all j cell 2, 2, and u₁,1 = 0.3, ui,2 = 0.5, U₁,3 = 0.8 for all i except cell 2, 2. In…arrow_forwardA boundary layer is a thin region (usually along a wall) in which viscous forces are significant and within which the flow is rotational. Consider a boundary layer growing along a thin flat plate. The flow is steady. The boundary layer thickness ? at any downstream distance x is a function of x, free-stream velocity V∞, and fluid properties ? (density) and ? (viscosity). Use the method of repeating variables to generate a dimensionless relationship for ? as a function of the other parameters. Show all your work.arrow_forwardWhich dimensionless parameter does not appear in the nondimensionalized Navier–Stokes equation? (a) Reynolds number (b) Prandtl number (c) Strouhal number (d ) Euler number (e) Froude numberarrow_forward
- As shown in the following figure, vortices are shed from the rear of a bluff cylinder placed across a flow. The vortices alternately leave the top and bottom of the cylinder, causing an alternating force normal to the freestream velocity. The vortex shedding frequency, f, depends on the fluid density p, width of the cylinder d, freestream velocity V, and fluid viscosity u. (a) Use Buckingham Pi Theorem to develop a functional relationship for f. Use M, L, t as the primary dimensional. Use p, V, and d as the repeating parameters. (b) Vortex shedding occurs in standard air on two cylinders with a diameter ratio of 2. Determine the velocity ratio for dynamic similarity, and the ratio of vortex shedding frequencies. -Vortices Varrow_forwardConsider a boundary layer growing along a thin flat plate. This problem involves the following parameters: boundary layer thickness ? , downstream distance x, free-stream velocity V, fluid density ? , and fluid viscosity ? . The number of primary dimensions represented in this problem is (a) 1 (b) 2 (c) 3 (d ) 4 (e) 5arrow_forwardOne model of the glomerular membrane is a microporous membrane in which right cylindrical porespenetrate all the way through the membrane. Assume that the pores have a length of 50 nm and aradius of 3.5 nm. The viscosity of plasma is 0.002 Pa s. The average hydrostatic pressure in theglomerulus is 60 mm Hg, hydrostatic pressure in Bowman’s space is 20 mm Hg and the averageoncotic pressure of glomerular capillary blood is 28 mm Hg.A. Calculate the flow through a single pore assuming laminar flow (use the Poiseuille flowequation).B. How many pores would there have to be to produce a normal GFR?C. If the total aggregate area of the kidneys for filtration is 1.5 m2, what is the density of thepores (number of pores per unit area)D. What fraction of the area is present as pores?arrow_forward
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