
Fluid Mechanics (2nd Edition)
2nd Edition
ISBN: 9780134649290
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 5, Problem 8P
To determine
The velocity and pressure of the water at point A.
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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 5 Solutions
Fluid Mechanics (2nd Edition)
Ch. 5 - Prob. 1FPCh. 5 - Oil is subjected to a pressure of 300 kPa at A,...Ch. 5 - Prob. 3FPCh. 5 - Water flows through the pipe at 8 m/s. Determine...Ch. 5 - The tank has a square base and is filled with...Ch. 5 - Prob. 6FPCh. 5 - Water flows from the reservoir through the...Ch. 5 - Crude oil flows through the 50-mm-diameter pipe...Ch. 5 - Water at A has a pressure of 400 kPa and a...Ch. 5 - Water from the reservoir flows through the...
Ch. 5 - Prob. 11FPCh. 5 - The jet engine takes in air and fuel having an...Ch. 5 - Determine the required average change in pressure...Ch. 5 - Prob. 2PCh. 5 - Prob. 3PCh. 5 - Air at 60°F flows through the horizontal tapered...Ch. 5 - Prob. 5PCh. 5 - The water in an open channel drainage canal flows...Ch. 5 - Water flows out of a faucet at A at 6 m/s....Ch. 5 - Water flows through the 30-mm-diameter pipe at...Ch. 5 - Water flows through the 30-mm-diameter pipe and is...Ch. 5 - Drainage under a canal is provided using a...Ch. 5 - Prob. 11PCh. 5 - Prob. 12PCh. 5 - A fountain is produced by water that flows up the...Ch. 5 - Prob. 14PCh. 5 - Air is drawn into the 200-mm-diameter cylinder...Ch. 5 - The level of mercury in the manometer has the...Ch. 5 - A fountain ejects water through the two nozzles A...Ch. 5 - Prob. 18PCh. 5 - Heavy rain has caused reservoir A to reach a...Ch. 5 - A fire hydrant supplies water under a pressure of...Ch. 5 - Determine the velocity of water through the pipe...Ch. 5 - The sewage siphon regulates the level of water in...Ch. 5 - If the manometer contains mercury, determine the...Ch. 5 - Prob. 24PCh. 5 - Prob. 25PCh. 5 - When the valve at A is opened, the initial...Ch. 5 - Prob. 27PCh. 5 - Prob. 28PCh. 5 - Air is pumped into the top of the tank so that the...Ch. 5 - Prob. 30PCh. 5 - Prob. 31PCh. 5 - A river has an average width of 5 m. Just after...Ch. 5 - A river has an average width of 5 m and flows with...Ch. 5 - Prob. 34PCh. 5 - Prob. 35PCh. 5 - Prob. 36PCh. 5 - Water flows through the transition at 0.3 m3/s,...Ch. 5 - If the water in piezometers A and B rises to hA =...Ch. 5 - Prob. 39PCh. 5 - Prob. 40PCh. 5 - Water flows through the pipe transition with a...Ch. 5 - Water from a faucet tapers from a diameter of 0.5...Ch. 5 - Prob. 43PCh. 5 - Prob. 44PCh. 5 - If the pressure at A is 325 kPa, and the velocity...Ch. 5 - If the pressure at A is 215 kPa, and the velocity...Ch. 5 - Prob. 47PCh. 5 - If the difference in the level of mercury within...Ch. 5 - Prob. 49PCh. 5 - Prob. 50PCh. 5 - Prob. 51PCh. 5 - If the pressure in the 6-in.-diameter pipe at A is...Ch. 5 - Prob. 53PCh. 5 - Prob. 54PCh. 5 - Prob. 56PCh. 5 - Prob. 57PCh. 5 - Prob. 58PCh. 5 - The solution is ejected from the 20-mm-diameter...Ch. 5 - Prob. 60PCh. 5 - Prob. 61PCh. 5 - Prob. 62PCh. 5 - Water from the large closed tank is to be drained...Ch. 5 - Prob. 64PCh. 5 - Carbon dioxide at 20°C passes through the...Ch. 5 - Prob. 66PCh. 5 - Prob. 67PCh. 5 - Determine the average velocity and the pressure in...Ch. 5 - Prob. 69PCh. 5 - Prob. 70PCh. 5 - Prob. 71PCh. 5 - Prob. 72PCh. 5 - Water at a pressure of 12 psi and a velocity of 5...Ch. 5 - Prob. 74PCh. 5 - Prob. 75PCh. 5 - The siphon spillway provides an automatic control...Ch. 5 - Prob. 77PCh. 5 - A piezometer and a manometer containing mercury...Ch. 5 - Water is drawn into the pump, such that the...Ch. 5 - Prob. 80PCh. 5 - Prob. 81PCh. 5 - Prob. 82PCh. 5 - Prob. 83PCh. 5 - A pump is used to deliver water from a large...Ch. 5 - A 6-hp pump with a 3-in.-diameter hose is used to...Ch. 5 - The pump is used with a 3-in.-diameter hose to...Ch. 5 - Solve Prob. 5–86 by including frictional head...Ch. 5 - The pump discharges water at B at 0.3 ft3/s. If...Ch. 5 - Prob. 89PCh. 5 - Draw the energy and hydraulic grade lines for the...Ch. 5 - The turbine removes energy from the water in the...Ch. 5 - Prob. 92PCh. 5 - Prob. 93PCh. 5 - Water in the reservoir flows through the...Ch. 5 - Prob. 95PCh. 5 - Determine the power delivered to the turbine if...Ch. 5 - The turbine at C draws a power of 90.5 hp. If the...Ch. 5 - Prob. 98PCh. 5 - Prob. 99PCh. 5 - Prob. 100PCh. 5 - The pump is connected to the 2-in.-diameter hose....Ch. 5 - Prob. 102PCh. 5 - Prob. 103PCh. 5 - Prob. 104PCh. 5 - Prob. 105PCh. 5 - Crude oil is pumped from a test separator at A to...Ch. 5 - Prob. 107PCh. 5 - Prob. 108PCh. 5 - Determine the power that the pump supplies to the...Ch. 5 - The pump delivers water at 120 ft3/min from the...Ch. 5 - Prob. 111PCh. 5 - Prob. 112P
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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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