FUNDAMENTALS OF FLUID MECHANICS
8th Edition
ISBN: 9781119571490
Author: GERHART
Publisher: WILEY
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Chapter 10.3, Problem 28P
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Problem 3: The inertia matrix can be written in dyadic form which is particularly useful
when inertia information is required in various vector bases. On the next page is a right
rectangular pyramid of total mass m. Note the location of point Q.
(a) Determine the inertia dyadic for the pyramid P, relative to point Q, i.e., 7%, for unit
vectors ₁₁, 2, 3.
Can you solve for v? Also, what is A x u
The external loads on the element shown below at the free end are F = 1.75 kN, P = 9.0
kN, and T = 72 Nm.
The tube's outer diameter is 50 mm and the inner diameter is 45 mm.
Given: A(the cross-sectional area) is 3.73 cm², Moment inertial I is 10.55 cm4, and J
polar moment inertial is 21.1 cm4.
Determine the following.
(1) The critical element(s) of the bar.
(2) Show the state of stress on a stress element for each critical element.
-120 mm-
F
Chapter 10 Solutions
FUNDAMENTALS OF FLUID MECHANICS
Ch. 10.2 - Prob. 1PCh. 10.2 - The flowrate per unit width in a wide channel is q...Ch. 10.2 - A rectangular channel 3 m wide carries 10 m3/s at...Ch. 10.2 - Prob. 4PCh. 10.2 - Prob. 5PCh. 10.2 - Prob. 6PCh. 10.2 - Prob. 7PCh. 10.2 - Prob. 8PCh. 10.2 - Prob. 9PCh. 10.2 - Prob. 10P
Ch. 10.2 - Prob. 11PCh. 10.3 - Water flows in a 10-m-wide open channel with a...Ch. 10.3 - Water flows in a 10-ft-wide rectangular channel...Ch. 10.3 - Water flows in a rectangular channel at a rate of...Ch. 10.3 - Water flows in a 5-ft-wide rectangular channel...Ch. 10.3 - Water flows over the bump in the bottom of the...Ch. 10.3 - Water in a rectangular channel flows into a...Ch. 10.3 - A channel has a rectangular cross section, a width...Ch. 10.3 - Prob. 19PCh. 10.3 - Prob. 20PCh. 10.3 - Prob. 23PCh. 10.3 - Prob. 24PCh. 10.3 - Prob. 25PCh. 10.3 - Prob. 26PCh. 10.3 - Prob. 27PCh. 10.3 - Prob. 28PCh. 10.3 - Prob. 29PCh. 10.4 - Water flows in a 5-m-wide channel with a speed...Ch. 10.4 - The following data are taken from measurements on...Ch. 10.4 - Prob. 32PCh. 10.4 - The following data are obtained for a particular...Ch. 10.4 - Prob. 34PCh. 10.4 - Prob. 35PCh. 10.4 - A 2-m-diameter pipe made of finished concrete lies...Ch. 10.4 - By what percent is the flowrate reduced in the...Ch. 10.4 - Prob. 38PCh. 10.4 - Prob. 39PCh. 10.4 - Prob. 40PCh. 10.4 - A trapezoidal channel with a bottom width of 3.0 m...Ch. 10.4 -
Water flows in a 2-m-diameter finished concrete...Ch. 10.4 - A round concrete storm sewer pipe used to carry...Ch. 10.4 - Find the discharge per unit width for a wide...Ch. 10.4 - Water flows down a wide rectangular channel having...Ch. 10.4 - Prob. 46PCh. 10.4 - Prob. 47PCh. 10.4 - Prob. 48PCh. 10.4 - Determine the flowrate for the symmetrical channel...Ch. 10.4 - (See The Wide World of Fluids article titled “Done...Ch. 10.4 - Prob. 51PCh. 10.4 - Prob. 52PCh. 10.4 - Prob. 53PCh. 10.4 - Prob. 54PCh. 10.4 - Prob. 55PCh. 10.4 - Prob. 56PCh. 10.4 - Prob. 57PCh. 10.4 - Prob. 58PCh. 10.4 - Prob. 59PCh. 10.4 - Prob. 60PCh. 10.4 - Prob. 61PCh. 10.4 - Prob. 62PCh. 10.4 - Prob. 63PCh. 10.4 - Water flows 1 m deep in a 2-m-wide finished...Ch. 10.4 - Uniform flow in a sluggish channel having a nearly...Ch. 10.4 - To prevent weeds from growing in a clean...Ch. 10.4 - Prob. 67PCh. 10.4 - Prob. 68PCh. 10.4 - Prob. 69PCh. 10.4 - Prob. 70PCh. 10.5 - Prob. 71PCh. 10.5 - Prob. 72PCh. 10.6 - Water flows upstream of a hydraulic jump with a...Ch. 10.6 - Prob. 75PCh. 10.6 - Prob. 76PCh. 10.6 - Prob. 77PCh. 10.6 - At a given location in a 12-ft-wide rectangular...Ch. 10.6 - Prob. 79PCh. 10.6 - Prob. 80PCh. 10.6 - Prob. 81PCh. 10.6 - A hydraulic engineer wants to analyze steady flow...Ch. 10.6 - Prob. 83PCh. 10.6 - A rectangular sharp-crested weir is used to...Ch. 10.6 - Prob. 85PCh. 10.6 - Prob. 87PCh. 10.6 - Prob. 88PCh. 10.6 - Prob. 89PCh. 10.6 - Prob. 90PCh. 10.6 - Prob. 91PCh. 10.7 - Prob. 1LLPCh. 10.7 - Prob. 2LLPCh. 10.7 - Prob. 3LLP
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- A crate weighs 530 lb and is hung by three ropes attached to a steel ring at A such that the top surface is parallel to the xy plane. Point A is located at a height of h = 42 in above the top of the crate directly over the geometric center of the top surface. Use the dimensions given in the table below to determine the tension in each of the three ropes. 2013 Michael Swanbom ↑ Z C BY NC SA b x B у D Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value a 30 in b 43 in с 4.5 in The tension in rope AB is lb The tension in rope AC is lb The tension in rope AD is lbarrow_forwardThe airplane weighs 144100 lbs and flies at constant speed and trajectory given by 0 on the figure. The plane experiences a drag force of 73620 lbs. a.) If = 11.3°, determine the thrust and lift forces required to maintain this speed and trajectory. b.) Next consider the case where is unknown, but it is known that the lift force is equal to 7.8 times the quantity (Fthrust Fdrag). Compute the resulting trajectory angle - and the lift force in this case. Use the same values for the weight and drag forces as you used for part a. Уллу Fdrag 10. Ө Fthrust cc 10 2013 Michael Swanbom BY NC SA Flift Fweight The lift force acts in the y' direction. The weight acts in the negative y direction. The thrust and drag forces act in the positive and negative x' directions respectively. Part (a) The thrust force is equal to lbs. The lift force is equal to Part (b) The trajectory angle is equal to deg. The lift force is equal to lbs. lbs.arrow_forwardThe hoist consists of a single rope and an arrangement of frictionless pulleys as shown. If the angle 0 = 59°, determine the force that must be applied to the rope, Frope, to lift a load of 4.4 kN. The three-pulley and hook assembly at the center of the system has a mass of 22.5 kg with a center of mass that lies on the line of action of the force applied to the hook. e ΘΕ B CC 10 BY NC SA 2013 Michael Swanbom Fhook Note the figure may not be to scale. Frope = KN HO Fropearrow_forward
- Determine the tension developed in cables AB and AC and the force developed along strut AD for equilibrium of the 400-lb crate. x. 5.5 ft C 2 ft Z 2 ft D 6 ft B 4 ft A 2.5 ftarrow_forwardA block of mass m hangs from the end of bar AB that is 7.2 meters long and connected to the wall in the xz plane. The bar is supported at A by a ball joint such that it carries only a compressive force along its axis. The bar is supported at end B by cables BD and BC that connect to the xz plane at points C and D respectively with coordinates given in the figure. Cable BD is elastic and can be modeled as a linear spring with a spring constant k = 400 N/m and unstretched length of 6.34 meters. Determine the mass m, the compressive force in beam AB and the tension force in cable BC. Z D (c, 0, d) C (a, 0, b), A e B y f m BY NC SA x 2016 Eric Davishahl Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value a 8.1 m b 3.3 m C 2.7 m d 3.9 m e 2 m f 5.4 m The mass of the block is The compressive force in bar AB is The tension in cable S is N. kg.arrow_forwardTwo squirrels are sitting on the rope as shown. The squirrel at A has a weight of 1.2 lb. The squirrel at B found less food this season and has a weight of 0.8 lb. The angles 0 and > are equal to 50° and 60° respectively. Determine the tension force in each of the rope segments (T₁ in segment, T₂ in segment Я, and T3 in segment DD) as well as the angle a in degrees. Ө A α B Note the figure may not be to scale. T₁ = lb lb T2 T3 = = lb απ deg A BY NC SA 2013 Michael Swanbomarrow_forward
- Each cord can sustain a maximum tension of 500 N. Determine the largest mass of pipe that can be supported. B 60° A E Harrow_forward2. Link BD consists of a single bar 1 in. wide and 0.5 in. thick. Knowing that each pin has a in. diameter, determine (a) the maximum value of the normal stress in link BD and the bearing stress in link BD if 0 = 0, (b) the maximum value of the normal stress in link BD if 0 = 90. -6 in.- 12 in. 30° D 4 kipsarrow_forwardIn the image is a right rectangular pyramid of total mass m. Note the location of point Q. Determine the inertia dyadic for the pyramid P, relative to point Q for e hat unit vectors.arrow_forward
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