Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
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Chapter 4, Problem 4.2WP
Is it true that the continuity relation, Eq. (4.6), is valid for both viscous and inviscid, new Ionian and nonnewtonian, compressible and incompressible flow? If so, are there any limitations on this equation?
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Chapter 4 Solutions
Fluid Mechanics
Ch. 4 - Prob. 4.1PCh. 4 - Flow through the converging nozzle in Fig. P4.2...Ch. 4 - Prob. 4.3PCh. 4 - Prob. 4.4PCh. 4 - Prob. 4.5PCh. 4 - Prob. 4.6PCh. 4 - Prob. 4.7PCh. 4 - P4.8 When a valve is opened, fluid flows in...Ch. 4 - An idealized incompressible flow has the proposed...Ch. 4 - A two-dimensional, incompressible flow has the...
Ch. 4 - Prob. 4.11PCh. 4 - Prob. 4.12PCh. 4 - Prob. 4.13PCh. 4 - Prob. 4.14PCh. 4 - What is the most general form of a purely radial...Ch. 4 - Prob. 4.16PCh. 4 - An excellent approximation for the two-dimensional...Ch. 4 - Prob. 4.18PCh. 4 - A proposed incompressible plane flow in polar...Ch. 4 - Prob. 4.20PCh. 4 - Prob. 4.21PCh. 4 - Prob. 4.22PCh. 4 - Prob. 4.23PCh. 4 - Prob. 4.24PCh. 4 - An incompressible flow in polar coordinates is...Ch. 4 - Prob. 4.26PCh. 4 - Prob. 4.27PCh. 4 - P4.28 For the velocity distribution of Prob. 4.10,...Ch. 4 - Prob. 4.29PCh. 4 - Prob. 4.30PCh. 4 - Prob. 4.31PCh. 4 - Prob. 4.32PCh. 4 - Prob. 4.33PCh. 4 - Prob. 4.34PCh. 4 - P4.35 From the Navier-Stokes equations for...Ch. 4 - A constant-thickness film of viscous liquid flows...Ch. 4 - Prob. 4.37PCh. 4 - Prob. 4.38PCh. 4 - Reconsider the angular momentum balance of Fig....Ch. 4 - Prob. 4.40PCh. 4 - Prob. 4.41PCh. 4 - Prob. 4.42PCh. 4 - Prob. 4.43PCh. 4 - Prob. 4.44PCh. 4 - Prob. 4.45PCh. 4 - Prob. 4.46PCh. 4 - Prob. 4.47PCh. 4 - Consider the following two-dimensional...Ch. 4 - Prob. 4.49PCh. 4 - Prob. 4.50PCh. 4 - Prob. 4.51PCh. 4 - Prob. 4.52PCh. 4 - Prob. 4.53PCh. 4 - P4.54 An incompressible stream function is...Ch. 4 - Prob. 4.55PCh. 4 - Prob. 4.56PCh. 4 - A two-dimensional incompressible flow field is...Ch. 4 - P4.58 Show that the incompressible velocity...Ch. 4 - Prob. 4.59PCh. 4 - Prob. 4.60PCh. 4 - An incompressible stream function is given by...Ch. 4 - Prob. 4.62PCh. 4 - Prob. 4.63PCh. 4 - Prob. 4.64PCh. 4 - Prob. 4.65PCh. 4 - Prob. 4.66PCh. 4 - A stream function for a plane, irrotational, polar...Ch. 4 - Prob. 4.68PCh. 4 - A steady, two-dimensional flow has the following...Ch. 4 - A CFD model of steady two-dimensional...Ch. 4 - Consider the following two-dimensional function...Ch. 4 - Prob. 4.72PCh. 4 - Prob. 4.73PCh. 4 - Prob. 4.74PCh. 4 - Given the following steady axisymmetric stream...Ch. 4 - Prob. 4.76PCh. 4 - Prob. 4.77PCh. 4 - Prob. 4.78PCh. 4 - Prob. 4.79PCh. 4 - Oil, of density and viscosity , drains steadily...Ch. 4 - Prob. 4.81PCh. 4 - Prob. 4.82PCh. 4 - P4.83 The flow pattern in bearing Lubrication can...Ch. 4 - Consider a viscous film of liquid draining...Ch. 4 - Prob. 4.85PCh. 4 - Prob. 4.86PCh. 4 - Prob. 4.87PCh. 4 - The viscous oil in Fig. P4.88 is set into steady...Ch. 4 - Oil flows steadily between two fixed plates that...Ch. 4 - Prob. 4.90PCh. 4 - Prob. 4.91PCh. 4 - Prob. 4.92PCh. 4 - Prob. 4.93PCh. 4 - Prob. 4.94PCh. 4 - Two immiscible liquids of equal thickness h are...Ch. 4 - Prob. 4.96PCh. 4 - Prob. 4.97PCh. 4 - Prob. 4.98PCh. 4 - For the pressure-gradient flow in a circular tube...Ch. 4 - W4.1 The total acceleration of a fluid particle is...Ch. 4 - Is it true that the continuity relation, Eq....Ch. 4 - Prob. 4.3WPCh. 4 - Prob. 4.4WPCh. 4 - W4.5 State the conditions (there are more than...Ch. 4 - Prob. 4.6WPCh. 4 - W4.7 What is the difference between the stream...Ch. 4 - Under what conditions do both the stream function...Ch. 4 - Prob. 4.9WPCh. 4 - Consider an irrotational, incompressible,...Ch. 4 - Prob. 4.1FEEPCh. 4 - Prob. 4.2FEEPCh. 4 - Prob. 4.3FEEPCh. 4 - Given the steady, incompressible velocity...Ch. 4 - Prob. 4.5FEEPCh. 4 - Prob. 4.6FEEPCh. 4 - C4.1 In a certain medical application, water at...Ch. 4 - Prob. 4.2CP
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- Extend the control volume analysis used to derive the continuity equation to three-dimensional unsteady flows and show that Eq. (2.2a) can be written as (P2.1) ap 3+ (pu) + (pv) + (pw) - 0. a axarrow_forward(a) Extend the control volume analysis used to derive the continuity equation to three-dimensional unsteady flows and show that Eq. (2.2a) can be written as (P2.1) ap + (pu) + (pv) + (pw) = 0. at (b) Deduce from Eq. (P2.1) the mass conservation equations for three-dimen- sional steady or unsteady constant-density flow and for three-dimensional steady, variable-density flows corresponding to Eqs. (2.2b) and (2.2c) for two-dimensional flows. (c) Show that Eq. (P2.1) can be rewritten as a transport equation for p, using the three-dimensional version of the d/dt operator defined in Eq. (2.10).arrow_forward1. Consider a three-dimensional steady incompressible flow with components: u =-x(y+z), v= y, w=÷(z²-2yz), (a) Is the flow locally rotating? Justify your answer. (b) Determine the equation of vortex lines. (c) Are the vortex lines perpendicular to the streamlines?arrow_forward
- 3. The two-dimensional velocity field in a fluid is given by V 2ri+ 3ytj. (i) Obtain a parametric = equation for the pathline of the particle that passed through (1.1) at t = 0. (ii) Without calculating any equation: if I were to draw the streak-line at t = 0 of all points that passed through (1, 1) would it be the same or different? Justify yourself.arrow_forwardImagine a steady, two-dimensional, incompressible flow that is purely circular in the xy- or r?-plane. In other words, velocity component u? is nonzero, but ur is zero everywhere. What is the most general form of velocity component u? that does not violate conservation of mass?arrow_forwardImagine a steady, two-dimensional, incompressible flow that is purely radial in the xy- or r?-plane. In other words, velocity component ur is nonzero, but u? is zero everywhere. What is the most general form of velocity component ur that does not violate conservation of mass?arrow_forward
- An excellent approximation for the two-dimensional incompressible laminar boundary layer on the flat surface in Fig. P4.17 is for y s8 where 8 = Cx2, C = const (a) Assuming a no-slip condition at the wall, find an expression for the velocity component v(x, y) for ys 8. (b) Then find the maximum value of vat the station x = 1 m, for the particular case of airflow, when U = 3 m/s and &= 1.1 cm. Layer thickness 5(x) U= constant и (х, у) u(x, y)arrow_forwardConsider 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_forward(5) Cansder the stdy-state flow of an incompressible Newtanian fluid througha harizartal tube of irner radius Randlength L, sshown beldow: Find the velocity distribution in the ligquid. Neglect endeffects.arrow_forward
- For an Eulerian flow field described by u = 2xyt, v = y3x/3, w = 0: (a) Is this flow one-, two-, or three-dimensional? (b) Is this flow steady? (c) Is this flow incompressible? (d) Find the x-component of the acceleration vector.arrow_forwardVelocity components u = (Axy³ – x²y), v = xy² . possible flow field involving steady incompressible flow is then value of 2 for (a) 0 (b) 1 (c) 2 (d) 3arrow_forwardAn idealized incompressible fl ow has the proposed threedimensionalvelocity distributionV = 4xy2i + f (y)j - zy2k Find the appropriate form of the function f ( y ) that satisfi esthe continuity relation.arrow_forward
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