Fluid Mechanics, 8 Ed
8th Edition
ISBN: 9789385965494
Author: Frank White
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Textbook Question
Chapter 6, Problem 6.53P
Water at 2OC flows by gravity through a smooth pipe from one reservoir to a lower one. The elevation difference is 60 m. The pipe ¡s 360 m long, with a diameter of 12 cm. Calculate the expected flow rate in m3/h. Neglect minor losses.
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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
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
D
3
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?
Chapter 6 Solutions
Fluid Mechanics, 8 Ed
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