Engineering Answers

1.) A and B are rolling cylinders connecting the shafts S and T. C and E are cylinders fast to these shafts and slipping on each other at P. Find the diameters of C and E if the surface speed of E is twice that of C.

2.) Two solids of right section 2 and 4 are in pure rolling contact between the circular arcs. What is the angular speed ratio for the position shown? Determine the size of the angles , β, and Ø in degrees, and of the radii x and y in inches.

3. Two shafts, having axes in the same plate intersecting at an angle of 45°, turn in opposite senses at 30 rpm and 90 rpm. Draw a pair of cone to be located on these shafts and turn in pure rolling contact. Diameter of base of smaller cone is 1 in. Calculate the cone angles.

4. Two shafts A and B are connected by rolling cones and turn in the same direction. Shaft A makes 300 rpm while shaft B makes 100 rpm. Calculate the cone angle of each cone and the diameter of each base if the base of cone B is 2 in. from the vertex. θ = 30°

1. Two parallel shafts, 11 in. apart and rotating at 75 rpm and 200 rpm, are connected by cylinders in pure

rolling contact. Determine the diameters of the cylinders: (1) when they turn in opposite directions; and (2)

when they turn in the same direction.

2. Two parallel shafts connected by rolling cylinders turn in the same direction 150 rpm and 100 rpm

respectively. The smaller cylinder is 16 in. in diameter. How far apart are the axes of the shafts?

3. Two parallel shafts, 24 inches apart and having a speed ratio of 3, are connected by cylinders in pure rolling

contact. Determine the diameters of the cylinders: (1) when they turn in opposite directions; and (2) when

they turn in the same direction

As a material engineer in charge of designing concrete mix and facing the following problems, which admixture would you use in each case during mixing or at the jobsite?

a. There is a large quantity of freshly mixed concrete and the work at the jobsite had to stop because of rain.

b. More time is expected to be needed for finishing concrete

c. The structure is subject to freezing

d. Concrete is to be around tightly spaced reinforcing steel

e. Concrete mix will be hauled a long distance

f. High early strength concrete is required, but not necessarily high ultimate strength

According to ASTM C94, are there other tests to be performed to evaluate the suitability of that water? Discuss briefly

The water-cement ratio is important because it influences all of the desirable qualities of concrete. Briefly describe how super high strength concrete (f'c = 15 ksi) can be made?

The water-cement ratio is important because it influences all of the desirable qualities of concrete. Why is the extra water necessary

The water-cement ratio is important because it influences all of the desirable qualities of concrete. What is the minimum water-cement ratio for hydration only?

The water-cement ratio is important because it influences all of the desirable qualities of concrete. What is the typical water-cement ratio for normal strength concrete?

Show that when a Bingham plastic fluid flows under laminar condition through a tube of radius R and length L the volumetric flow rate, Q is given by 4 4 0 0 0 0 ( ) 4 1 1 8 3 3 L R R P P R Q L         −     = − +               Where 0  and R  are the yield stress and shear stress at the tube wall, respectively.

In a gas absorption experiment a viscous fluid flows upward through a small circular tube and then downward in laminar flow on the outside. Set up a momentum balance over a shell of thickness r in the film, as shown in figure 1 (Appendix A). Note that the “momentum in” and “momentum out” arrows are always taken in the positive coordinate direction, even though in this problem the momentum is flowing through the cylindrical surfaces in the negative r direction. i. Show that the velocity distribution in the falling film (neglecting end effects) is 2 2 2 1 2 ln 4 z gR r r v a R R         = − +               ii. Show that the mass rate of flow in the film is given by 2 4 2 4 4 1 4 3 4 ln 8 gR w a a a a   = − + − +     iii. Show that the result in (b) simplifies to the following equation, if the film thickness is very small ( Use a = +  1 , 1   ) 2 3 cos 3 gW w     = , Where W R = 2 and   = R .