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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Textbook Question
Chapter 7, Problem 125P
The primary dimensions of kinematic viscosity are
(a)
(b)
(c)
(d)
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what will be the kinematic viscosity of an oil having density 888 kg/m. The shear stress at a point in oil is 0.278 N/m and velocity gradient at that point is 0.2 per second.
Tutorial Problem #3.
As we discussed in lecture, a concentric cylinder
viscometer is often used to measure the viscosity
(μ) of Newtonian fluids. As shown in the
accompanying figure, the outer cylinder (with
radius Ro) remains stationary while the inner
cylinder (with radius R₁) rotates at an angular
velocity of w (rev/min) and the torque (T) required
to rotate the inner cylinder is measured.
Outer Cylinder
Fluid
Inner Cylinder
T
ω
R₁
R
a. Starting from Newton's law of viscosity, derive the correct equation that is used to calculate u in
μ
terms of w, T, Ro, R₁ and € (the height of the fluid in the gap between the two cylinders). Because
the radial distance between the cylinders (i.e Ro - R₁) is quite small, you can assume that the velocity
profile of the fluid varies linearly with respect to distance between the cylinders.
HINT #1: Torque is the required force multiplied by the moment arm (which is R¡ in this case)
HINT #2: Multiply the angular velocity by the circumference of the…
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Chapter 7 Solutions
Fluid Mechanics: Fundamentals and Applications
Ch. 7 - What is the difference between a dimension and a...Ch. 7 - List the seven primary dimensions. What is...Ch. 7 - Write the primary dimensions of the universal...Ch. 7 - Write the primary dimensions of each of the...Ch. 7 - Prob. 5PCh. 7 - Prob. 6PCh. 7 - Prob. 7PCh. 7 - On a periodic chart of the elements, molar mass...Ch. 7 - Prob. 9PCh. 7 - The moment of force(M)is formed by the cross...
Ch. 7 - You are probably familiar with Ohm law for...Ch. 7 - Write the primary dimensions of each of the...Ch. 7 - Prob. 13PCh. 7 - Thermal conductivity k is a measure of the ability...Ch. 7 - Write the primary dimensions of each of the...Ch. 7 - Prob. 16PCh. 7 - Explain the law of dimensional homogeneity in...Ch. 7 - Prob. 18PCh. 7 - Prob. 19PCh. 7 - An important application of fluid mechanics is the...Ch. 7 - Prob. 21PCh. 7 - Prob. 22PCh. 7 - In Chap. 4, we defined the material acceleration,...Ch. 7 - Newton's second law is the foundation for the...Ch. 7 - What is the primary reason for nondimensionalizing...Ch. 7 - Prob. 26PCh. 7 - In Chap. 9, we define the stream function for...Ch. 7 - In an oscillating incompressible flow field the...Ch. 7 - Prob. 29PCh. 7 - Consider ventilation of a well-mixed room as in...Ch. 7 - In an oscillating compressible flow field the...Ch. 7 - List the three primary purposes of dimensional...Ch. 7 - List and describe the three necessary conditions...Ch. 7 - A student team is to design a human-powered...Ch. 7 - Repeat Prob. 7-34 with all the same conditions...Ch. 7 - This is a follow-tip to Prob. 7-34. The students...Ch. 7 - The aerodynamic drag of a new sports car is lo be...Ch. 7 - This is a follow-tip to Prob. 7-37E. The...Ch. 7 - Consider the common situation in which a...Ch. 7 - Prob. 40PCh. 7 - Some students want to visualize flow over a...Ch. 7 - A lightweight parachute is being designed for...Ch. 7 - Prob. 43PCh. 7 - Prob. 44PCh. 7 - Prob. 45PCh. 7 - The Richardson number is defined as Ri=L5gV2...Ch. 7 - Prob. 47PCh. 7 - Prob. 48PCh. 7 - A stirrer is used to mix chemicals in a large tank...Ch. 7 - Prob. 50PCh. 7 - Albert Einstein is pondering how to write his...Ch. 7 - Consider filly developed Couette flow-flow between...Ch. 7 - Consider developing Couette flow-the same flow as...Ch. 7 - The speed of sound c in an ideal gas is known to...Ch. 7 - Repeat Prob. 7-54, except let the speed of sound c...Ch. 7 - Repeat Prob. 7-54, except let the speed of sound c...Ch. 7 - Prob. 57PCh. 7 - When small aerosol particles or microorganisms...Ch. 7 - Prob. 59PCh. 7 - Prob. 60PCh. 7 - Prob. 61PCh. 7 - An incompressible fluid of density and viscosity ...Ch. 7 - Prob. 63PCh. 7 - In the study of turbulent flow, turbulent viscous...Ch. 7 - Bill is working on an electrical circuit problem....Ch. 7 - A boundary layer is a thin region (usually along a...Ch. 7 - A liquid of density and viscosity is pumped at...Ch. 7 - A propeller of diameter D rotates at angular...Ch. 7 - Repeat Prob. 7-68 for the case an which the...Ch. 7 - Prob. 70PCh. 7 - Prob. 71PCh. 7 - Consider a liquid in a cylindrical container in...Ch. 7 - Prob. 73PCh. 7 - One of the first things you learn in physics class...Ch. 7 - Prob. 75CPCh. 7 - Prob. 76CPCh. 7 - Define wind tunnel blockage. What is the rule of...Ch. 7 - Prob. 78CPCh. 7 - Prob. 79CPCh. 7 - In the model truck example discussed in Section...Ch. 7 - Prob. 83PCh. 7 - A small wind tunnel in a university's...Ch. 7 - There are many established nondimensional...Ch. 7 - Prob. 86CPCh. 7 - For each statement, choose whether the statement...Ch. 7 - Prob. 88PCh. 7 - Prob. 89PCh. 7 - Prob. 90PCh. 7 - Prob. 91PCh. 7 - From fundamental electronics, the current flowing...Ch. 7 - Prob. 93PCh. 7 - Prob. 94PCh. 7 - The Archimedes number listed in Table 7-5 is...Ch. 7 - Prob. 96PCh. 7 - Prob. 97PCh. 7 - Prob. 98PCh. 7 - Prob. 99PCh. 7 - Prob. 100PCh. 7 - Repeal Prob. 7-100 except for a different...Ch. 7 - A liquid delivery system is being designed such...Ch. 7 - Prob. 103PCh. 7 - Au aerosol particle of characteristic size DPmoves...Ch. 7 - Prob. 105PCh. 7 - Prob. 106PCh. 7 - Prob. 107PCh. 7 - Prob. 108PCh. 7 - Prob. 109PCh. 7 - Prob. 110PCh. 7 - Repeat pall (a) of Prob. 7-110, except instead of...Ch. 7 - Sound intensity I is defined as the acoustic power...Ch. 7 - Repeal Prob. 7-112, but with the distance r from...Ch. 7 - Engineers at MIT have developed a mechanical model...Ch. 7 - Prob. 116PCh. 7 - Prob. 117PCh. 7 - An electrostatic precipitator (ESP) is a device...Ch. 7 - Prob. 119PCh. 7 - Prob. 120PCh. 7 - Prob. 121PCh. 7 - Prob. 122PCh. 7 - Prob. 123PCh. 7 - Prob. 124PCh. 7 - The primary dimensions of kinematic viscosity are...Ch. 7 - There at four additive terms in an equation, and...Ch. 7 - Prob. 127PCh. 7 - Prob. 128PCh. 7 - Prob. 129PCh. 7 - A one-third scale model of a car is to be tested...Ch. 7 - Prob. 131PCh. 7 - A one-third scale model of an airplane is to be...Ch. 7 - Prob. 133PCh. 7 - Prob. 134PCh. 7 - Consider a boundary layer growing along a thin...Ch. 7 - Prob. 136P
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- The physical model of a pipe containing water with kinematic viscosity o = 0.804 × 10-6 ™* has been built in the scale of in a laboratory. i. Find the ratio of velocity of water in the main pipe with kinematic viscosity of 8 = 2.79 x 10-4 m? to the model. ii. Discuss the difference in the velocities of the model and main pipe.arrow_forwardThe sliding plate viscometer shown below is used to measure the viscosity of a fluid. The top plate is moving to the right with a constant velocity of 10 m s in response to a force of 3 N. The bottom plate is stationary. What is the viscosity of the fluid? Assume a linear velocity distribution.arrow_forwardvalg, (21535mm 1.15 The pressure difference, Ap, across a partial blockage in an artery (called a stenosis) is approximated by the equation μV Ap - K. 4 + K.(A-1) pv² = K₂ A s.r to zogy nish190 32\V as bonb dignol a 3 basiy noft where V is the blood velocity, u the blood viscosity (FL-2T), p the blood density (ML), D the artery diameter, Ao the area of the unobstructed artery, and A, the area of the stenosis. Determine the dimensions of the constants K, and K. Would this equation be valid in any system of units?arrow_forward
- The Ekman number, Ek, arises in geophysical fluiddynamics. It is a dimensionless parameter combining seawaterdensity ρ , a characteristic length L , seawaterviscosity μ , and the Coriolis frequency Ω sin φ , where Ωis the rotation rate of the earth and φ is the latitude angle.Determine the correct form of Ek if the viscosity is in thenumerator.arrow_forwardThe kinematic viscosity of liquid oil (10³) C.S (1 stoke =100 C.S) and relative density = 0.92. Find the viscosity of the fluid oil in c.g.s and SI %3D systems.arrow_forwardThe primary dimensions of the universal gas constant Ru are (a) m·L/t2·T (b) m2·L/N (c) m·L2/t2·N·T (d ) L2/t2·T (e) N/m·tarrow_forward
- 1. For the shown conic body which rotating with constant angular velocity 10 rad/s, find the torque which effected by viscosity of the oil that surrounding the conic body. Take: Radius of the cone is 2 in Height of the cone is 4 in Oil viscosity is 3.125x107 lb.s/in? Answer : Torque =0.02535 lb. In P10 rad/s 0.01-in film 0.01 inarrow_forwardThe absolute viscosity of the liquid is 1.8 x 10^-3 Pa-s and its SG is 2.50. Compute the equivalent kinematic viscosity in m2/s (decimal form)arrow_forwardB1. Determine the kinematic viscosity of the fluid between the plates as shown in Figure B1 given the following information: F = 5N h = 0.5mm v = 7m/s L=21 cm w = 10cm SG= 0.80 Moving plate Stationary plate Fluid Figure B1 Varrow_forward
- الواجب الثاني خواص الموائع ثاني طرق Exl: The density of an oil is 850 kg/m³. Find the relative density and kinematic viscosity if the dynamic viscosity is 5*103 pa.s.arrow_forwardFor the capillary-tube viscometer shown, the liquid to be tested is drawn into the tube to the level of the top etched line. The time is then obtained for the liquid to drain to the bottom etched line. The kinematic viscosity, v, in m?/s is then obtained from the equation v = KR*t where K is a constant, R is the radius of the capillary tube in mm, and tis the drain time in seconds. When glycerin, whose viscosity is 1.4 Pa.s at 20°C and density is 260 kg/m³, is used as a calibration fluid in a particular viscometer the drain time is density of 970 kg/m3 is tested in the same viscometer the drain time is 900 s. What is the dynamic viscosity of this liquid? Glass strengthening bridge Etched lines 430 s. When a liquid having a Capillary tubearrow_forward2.27 Fluids of viscosities µ1 = 0.1 N s/m2 and 42 = 0.15 N s/m2 are contained between two plates (each plate is 1 m? in area). The thicknesses are h1 = 0.5 mm and h2 = 0.3 mm, respectively. And the upper plate moves at a velocity of 1.5 m/s. Determine the force required to move the upper plate and the fluid velocity at the interface between the two fluids. F, V h2 H2 h1 P2.27 Hint: Both Velocity and Shear stress are continuous at the fluid-fluid interface.arrow_forward
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