Fluid mechanics for Chemical Engineers 3rd. Edition by James O. Wilkes, Stacy G. Birmingham | 9780134712826 | 013471282X | Holooly

Fluid mechanics for Chemical Engineers [EXP-22145]

79 SOLVED PROBLEMS

Question: 5.7

Alternative Derivation of the Continuity Equation There are other, equivalent ways of deriving the continuity equation. To illustrate, derive the continuity equation in vector form by following the motion of a fluid element of constant mass, whose volume may be changing, as shown in Fig. E5.7, alon

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Focus attention when the element is at location B,...

Question: 5.3

An Alternative to the Differential Element When performing operations similar to the above, some people prefer first to consider a finite volume, such as one of dimensions Δx × Δy × Δz, and then let this shrink to one of differential size. Investigate this alternative.

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The net rate of outflow across the faces normal to...

Question: 6.9

Analysis of a Cone-and-Plate Rheometer The problem concerns the analysis of a cone-and-plate rheometer, an instrument developed and perfected in the 1950s and 1960s by Prof. Karl Weissenberg, for measuring the viscosity of liquids, and also known as the “Weissenberg rheogoniometer.”^4 A cross sectio

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Assumptions and the continuity equation. The follo...

Question: 1.7

Application of Archimedes’ Law Consider the situation in Fig. E1.7(a), in which a barrel rests on a raft that floats in a swimming pool. The barrel is then pushed off the raft and may either float or sink, depending on its contents and hence its mass. The cross-hatching shows the volumes of water t

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Initial state. Let the masses of the raft and barr...

Question: 8.3

Boundary-Layer Flow Between Parallel Plates (COMSOL) This example is essentially a reproduction, on our part, of one of the sample problems that was part of the COMSOL Model Library of several years ago, and we are indebted to COMSOL for the idea. A fluid of density 1,000 kg/m^3 and viscosity 0.01

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See Chapter 14 for more details about COMSOL Multi...

Question: 12.1

Calculation of Reynolds Numbers Calculate the Reynolds number Re for the following. Assume that the fluid has properties of water: density ρ = 1,000 kg/m^3, viscosity μ = 10^−3 kg/m s, and kinematic viscosity ν = 10^−6 m^2/s. Flow of drugs injected using thumb pressure (about 5 atm) on a 5-ml syrin

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Syringe: Because of the high pressure drop, we ant...

Question: 7.3

Combination of a Uniform Stream and a Line Sink (C) An inviscid fluid flows with velocity U parallel to a wall, as shown in Fig. E7.3.1. The narrow slot S is long in the direction normal to the diagram, and a volumetric flow rate Q per unit slot length is withdrawn. (The particle shown at x = X is

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The overall stream function is the sum of the stre...

Question: 5.8

Constant-Viscosity Momentum Balances in Terms of Velocity Gradients Verify the first of the three momentum balances of Eqn. (5.67) by starting from the x momentum balance of Eqn. (5.54) and substituting for the stresses σxx, τyx, and τzx from Eqns. (5.60) and (5.61).

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The indicated substitution leads to:

\begin...

Question: 14.2

Drawing a Complex Shape (COMSOL) Introduction We wish to draw the region depicted in Fig. 14.21, which is needed in Example 11.3 for solving non-Newtonian flow in an extrusion die. Briefly, we shall draw two overlapping rectangles and cut out or subtract from them two other regions known as “Bézier

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Procedure All mouse clicks are left-click ("Select...

Question: 12.4

Electroosmosis in a Microchannel (COMSOL) The microchannel ABCD in Fig. E12.4.1, with length L = 5 × 10^−4 m and width H = 5× 10^−5 m, contains an electrically conducting liquid whose physical properties are given in Table E12.4.1, in which “S” denotes units of Siemens, also equivalent to ohm^−1. N

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See Chapter 14 for more details about COMSOL Multi...

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