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Modern Fluid Dynamics: Basic Theory and Selected Applications in Macro- and Micro-Fluidics

85 SOLVED PROBLEMS

Question: 3.1

A-D: Physical Insight Gained from Solving Bernoulli’s Equation. (A) Why do airplanes fly? (B) Why do roofs fly off houses during tornadoes? (C) Estimate the wind force on a highrise window. (D) Consider an oscillating disk suspended on a fluid jet A horizontal disk of mass M can only move ...

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(A) Well, they need a lift force larger than the p...
Question: 2.12

Scale Analyses (for readers who like heat transfer) Task A: Scale Natural Convection on a Vertical Wall Consider steady laminar “natural convection” where, for example, air near a heated vertical wall rises against gravity. Within that thin thermal wall layer, the governing equations are (see ...

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(i) Replacing the variables u, v, x, y, and T by [...
Question: 3.5

Parallel Flows in Cylindrical Tubes Case A: Consider flow through an annulus with tube radius R and inner concentric cylinder aR, where a < 1, creating a ring-like crosssectional flow area. ...

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Case A: Of interest is the z-momentum equation, i....
Question: 3.18

Turbulent Thermal Pipe Flow Consider fully-developed hot air flow in a metal tube (m = 0.05 kg/s; L = 5 m; D = 0.15 m ). Because of the cold ambient (T∞ = 0°C, hambient = 6 W/m²K), the air inlet temperature T1 = 103°C drops to T2 = 77°C at the tube outlet. Find the heat loss and surface temperature ...

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• Properties (App. B) for T_{\rm ref}[/late...
Question: 3.8

Evaluation of the Hydraulic Conductivity As discussed, a possible porous-medium model is a structure with n parallel tubes of diameter d, representing straight pores or capillaries. Assuming steady laminar fully-developed flow in horizontal tubes, find an expression for K= æ /μ. ...

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Using Eq. (E.3.4.7a) to obtain the flow rate per p...
Question: 1.4

Determine the viscosity of a fluid in a basic cone-plate viscometer with given cone angle and radius, applied torque and resulting constant angular velocity. Plot the result as T = T(R,μ ). ...

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• From the graph, the linear circumferential veloc...
Question: 2.1

Volumetric Flow Rate Consider a liquid-filled tank (depth H) with a horizontal slot outlet (height 2h and width w) where the locally varying outlet velocity can be expressed as (see Sketch): u ≈ √2g (H − z) A constant fluid mass flow rate, min, is added to maintain the liquid depth H. The ...

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The u(z)-equation will be derived in Sect. 2.3.2. ...
Question: 2.2

Multi-port Flow Junction Consider a feed pipe ( A, v1 ) bifurcating into two outlet pipes (A2 , v2 and A3 , v3 ) where a small hole ( A4 ) has been detected in the junction area. Develop an equation for the leak  Q4. ...

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The fact that the inlet/outlet velocities are all ...
Question: 2.3

Draining of a Tank: A “deformable C.∀.” because the fluid level decreases and hence we have a shrinking C.∀. with moving C.S Consider a relatively small tank of diameter D and initially filled to height h0. The fluid drains through a pipe of radius (r0) according to: u(r) = 2u[1-(r/r0)²] (see ...

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Equation (2.8b) can be expanded for this problem w...
Question: 2.4

Use of the Continuity Equation (Two Problems: A and B) (A) For steady laminar fully-developed pipe flow of an incompressible fluid (see Sect. 2.4), the axial flow is: vz (r) = vmax [1 – (r/r0)²] (E.2.4.1) Show that the radial (or normal) velocity vr = 0. ...

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(A) Based on the assumptions, Eq. (2.10) is approp...
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