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 7, Problem 79CP
To determine
The rule of thumb about Mach number. Also, state wind tunnel results are incorrect if the rule of thumb is violated.
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Students have asked these similar questions
The gears shown in the figure have a diametral pitch of 2 teeth per inch and a 20° pressure angle.
The pinion rotates at 1800 rev/min clockwise and transmits 200 hp through the idler pair to gear
5 on shaft c. What forces do gears 3 and 4 transmit to the idler shaft?
TS
I
y
18T
32T
This
a
12
x
18T
C
48T
5
Question 1. Draw 3 teeth for the following pinion and gear respectively. The teeth
should be drawn near the pressure line so that the teeth from the pinion should
mesh those of the gear. Drawing scale (1:1). Either a precise hand drawing or
CAD drawing is acceptable. Draw all the trajectories of the involute lines and the
circles.
Specification: 18tooth pinion and 30tooth gear. Diameter pitch=P=6 teeth /inch.
Pressure angle:20°, 1/P for addendum (a) and 1.25/P for dedendum (b). For fillet,
c=b-a.
5. The figure shows a gear train. There is no friction at the bearings except for the gear tooth forces.
The material of the milled gears is steel having a Brinell hardness of 170. The input shaft speed (n2)
is 800 rpm. The face width and the contact angle for all gears are 1 in and 20° respectively. In this
gear set, the endurance limit (Se) is 15 kpsi and nd (design factor) is 2.
(a) Find the revolution speed of gear 5.
(b) Determine whether each gear satisfies the design factor of 2.0 for bending fatigue.
(c) Determine whether each gear satisfies the design factor of 2.0 for surface fatigue (contact stress).
(d) According to the computation results of the questions (b) and (c), explain the possible failure
mechanisms for each gear.
N4=28
800rpm
N₁=43
N5=34
N₂=14
P(diameteral pitch)=8 for all gears
Coupled to 2.5hp motor
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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- 1. The rotating steel shaft is simply supported by bearings at points of B and C, and is driven by a spur gear at D, which has a 6-in pitch diameter. The force F from the drive gear acts at a pressure angle of 20°. The shaft transmits a torque to point A of TA =3000 lbĘ in. The shaft is machined from steel with Sy=60kpsi and Sut=80 kpsi. (1) Draw a shear force diagram and a bending moment diagram by F. According to your analysis, where is the point of interest to evaluate the safety factor among A, B, C, and D? Describe the reason. (Hint: To find F, the torque Tд is generated by the tangential force of F (i.e. Ftangential-Fcos20°) When n=2.5, K=1.8, and K₁ =1.3, determine the diameter of the shaft based on (2) static analysis using DE theory (note that fatigue stress concentration factors need to be used for this question because the loading condition is fatigue) and (3) a fatigue analysis using modified Goodman. Note) A standard diameter is not required for the questions. 10 in Darrow_forward3 N2=28 P(diametral pitch)=8 for all gears Coupled to 25 hp motor N3=34 Full depth spur gears with pressure angle=20° N₂=2000 rpm (1) Compute the circular pitch, the center-to-center distance, and base circle radii. (2) Draw the free body diagram of gear 3 and show all the forces and the torque. (3) In mounting gears, the center-to-center distance was reduced by 0.1 inch. Calculate the new values of center-to-center distance, pressure angle, base circle radii, and pitch circle diameters. (4)What is the new tangential and radial forces for gear 3? (5) Under the new center to center distance, is the contact ratio (mc) increasing or decreasing?arrow_forward2. A flat belt drive consists of two 4-ft diameter cast-iron pulleys spaced 16 ft apart. A power of 60 hp is transmitted by a pulley whose speed is 380 rev/min. Use a service factor (Ks) pf 1.1 and a design factor 1.0. The width of the polyamide A-3 belt is 6 in. Use CD=1. Answer the following questions. (1) What is the total length of the belt according to the given geometry? (2) Find the centrifugal force (Fc) applied to the belt. (3) What is the transmitted torque through the pulley system given 60hp? (4) Using the allowable tension, find the force (F₁) on the tight side. What is the tension at the loose side (F2) and the initial tension (F.)? (5) Using the forces, estimate the developed friction coefficient (f) (6) Based on the forces and the given rotational speed, rate the pulley set. In other words, what is the horse power that can be transmitted by the pulley system? (7) To reduce the applied tension on the tight side, the friction coefficient is increased to 0.75. Find out the…arrow_forward
- The tooth numbers for the gear train illustrated are N₂ = 24, N3 = 18, №4 = 30, №6 = 36, and N₁ = 54. Gear 7 is fixed. If shaft b is turned through 5 revolutions, how many turns will shaft a make? a 5 [6] barrow_forwardCE-112 please solve this problem step by step and give me the correct answerarrow_forwardCE-112 please solve this problem step by step and give me the correct answerarrow_forward
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