A cylinder of diameter 10 cm rotates concentrically inside another hollowcylinder of inner diameter 10.1 cm. Both cylinders are 20 cm long and stand with theiraxis vertical. The annular space is filled with oil. If a torque of 100 kg cm is required torotate the inner cylinder at 100 rpm, determine the viscosity of oil. Ans. μ= 29.82poise

Answered: Image /qna-images/answer/e82719bb-3501-4ead-b53a-2f5d3e7099da.jpg

Answered: A cylinder of diameter 10 cm rotates…

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter11: Nonlinear Programming

Section: Chapter Questions

Problem 21RP

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(Conversion) An object’s polar moment of inertia, J, represents its resistance to twisting. For a cylinder, this moment of inertia is given by this formula: J=mr2/2+m( l 2 +3r 2 )/12misthecylindersmass( kg).listhecylinderslength(m).risthecylindersradius(m). Using this formula, determine the units for the cylinder’s polar moment of inertia.
(Civil eng.) The maximum load that can be placed at the end of a symmetrical wooden beam, such as the rectangular beam shown in Figure 2.20, can be calculated as the following: L=S1dc L is the maximum weight in lbs of the load placed on the beam. S is the stress in lbs/in2. I is the beam’s rectangular moment of inertia in units of in4. d is the distance in inches that the load is placed from the fixed end of the beam (the “moment arm”). c is one-half the height in inches of the symmetrical beam. For a 2” × 4” wooden beam, the rectangular moment of inertia is given by this formula: I=baseheight3=12=24312=10.674 c=(4in)=2in a. Using this information, design, write, compile, and run a C++ program that computes the maximum load in lbs that can be placed at the end of an 8-foot 24 wooden beam so that the stress on the fixed end is 3000lb/in2. b. Use the program developed in Exercise 9a to determine the maximum load in lbs that can be placed at the end of a 3” × 6” wooden beam so that the stress on the fixed end is 3000lb/in2.
(Conversion) Determine which of the following equations can’t be valid because they yield incorrect unit measurements: a.F=mab.F=m( v 2 /t)c.d=( at 2 )d.d=vte.F=mvtF=force(N)m=mass( kg)a=acceleration( m/s 2 )v=velocity( m/s)t=time(s)
(Practice) State whether the following variable names are valid. If they are invalid, state the reason. prod_a c1234 abcd _c3 12345 newamp watts $total new$al a1b2c3d4 9ab6 sum.of average volts1 finvolt
(Oceanography) The pressure, P, exerted on an underwater object can be determined by this formula: P=gh is the density of water, which is 1.94slug/ft3 . g is the acceleration caused by Earth’s gravity, which is 32.2ft/sec2. h is the object’s depth in the water in feet. a. Determine the units of P by calculating the units resulting from the right side of the formula. Check that your answer corresponds to the units for pressure listed in Table 1.1. b. Determine the pressure on a submarine operating at a depth of 2500 feet.
(Thermodynamics) The work, W, performed by a single piston in an engine can be determined by this formula: W=Fd F is the force provided by the piston in Newtons. d is the distance the piston moves in meters. a. Determine the units of W by calculating the units resulting from the right side of the formula. Check that your answer corresponds to the units for work listed in Table 1.1. b. Determine the work performed by a piston that provides a force of 1000 N over a distance of 15 centimeters.
(Numerical analysis) Here’s a challenging problem for those who know a little calculus. The Newton-Raphson method can be used to find the roots of any equation y(x)=0. In this method, the (i+1)stapproximation,xi+1,toarootofy(x)=0 is given in terms of the ith approximation, xi, by the following formula, where y’ denotes the derivative of y(x) with respect to x: xi+1=xiy(xi)/y(xi) For example, if y(x)=3x2+2x2,theny(x)=6x+2 , and the roots are found by making a reasonable guess for a first approximation x1 and iterating by using this equation: xi+1=xi(3xi2+2xi2)/(6xi+2) a. Using the Newton-Raphson method, find the two roots of the equation 3x2+2x2=0. (Hint: There’s one positive root and one negative root.) b. Extend the program written for Exercise 6a so that it finds the roots of any function y(x)=0, when the function for y(x) and the derivative of y(x) are placed in the code.
(Practice) a. To convert inches (in) to feet (ft), the number of inches should be multiplied by which of the following conversion factors? i. 12 in/1 ft ii. 1 ft/12 in b. To convert feet (ft) to meters (m), the number of feet should be multiplied by which of the following conversion factors? i. 1 m/3.28 ft ii. 3.28 ft/1 m c. To convert sq.yd to sq.ft, the number of sq.yd should be multiplied by which of the following conversion factors? i. 1 sq.yd/9 sq.ft ii. 9 sq.ft/1 sq.yd d. To convert meters (m) to kilometers (km), the number of meters should be multiplied by which of the following conversion factors? i. 1000 m/1 km ii. 1 km/1000 m e. To convert sq.in to sq.ft, the number of sq.in should be multiplied by which of the following conversion factors? i. 144 sq.in/1 sq.ft ii. 1 sq.ft/144 sq.in f. To convert minutes (min) to seconds (sec), the number of minutes should be multiplied by which of the following conversion factors? i. 60 sec/1 min ii. 1 min/60 sec g. To convert seconds (sec) to minutes (min), the number of seconds should be multiplied by which of the following conversion factors? i. 60 sec/1 min ii. 1 min/60 sec

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