For fluid undergoing circular motion, the centripetal force is provided by a pressure difference. Consider a fluid element (density p) at radial distance r, which has thickness dr in the radial direction and surface area dA normal to the radial direction. The pressure difference gives rise to a force on the fluid element equal to (p(r + dr) – p(r))dA. (i) Equating the pressure difference to the centripetal force, find an expression for the radial pressure gradient in terms of p, r, and fluid velocity v.

A cylindrical pressure vessel having a radius r = 14 in. and wall thickness t = 0.375 in. is subjected to internal pressure p = 375 psi. In addition, a torque T = 90 kip-ft acts at each end of the cylinder (see figure). (Assume that the structures behave linearly elastically and that the stresses caused by two or more loads may be superimposed to obtain the resultant stresses acting at a point. Consider both in-plane and out-of-plane shear stresses unless otherwise specified.) (a) Determine the maximum tensile stress omay and the maximum in-plane shear stress Tmay in the wall of the cylinder. (Enter the magnitudes in ksi.) o, = ksi Tmax ksi (b) If the allowable in-plane shear stress is 4.5 ksi, what is the maximum allowable torque T? (Enter the magnitude in kip-ft.) kip-ft (c) If T = 150 kip-ft and allowable in-plane shear and allowable normal stresses are 4.5 ksi and 11.5 ksi, respectively, what is the minimum required wall thickness (in inches)? in.

A differential element on the bracket is subjected to plane strain that has the following components: , strain at x = 250 x 10-6, strain at y = 300 x 10-6,  strain at x y= -500 x 10-6. Use the strain-transformation equations and determine the normal strain strain x' in the x' direction on an element oriented at an angle of 35°. Note, a positive angle is counter clockwise.

Please correct my understanding of this question. -In the equation of the moment at point A, there is a value, 36(11.5). I assume that is a force from the distributed load. -If you are finding the moment at point A, wouldn't you only need one value from the distributed load which is 27(10)? So my question is how do you get the value of 36 and 11.5, separately. And what is it for?

Fluid flows past the two dimensional bar shown in figure. The pressures on the ends of the bar are as shown, and the average shear stress on the top and bottom of the bar is tavg. Assume that the drag due to pressure is equal to the drag due to viscous effects, the ratio between the average shear stress and the dynamic pressure is p = -0.2 U Width =b Tave -10h

An element in plane stress is subjected to stresses σ_x, σ_y, and τ_xy (see figure). Using Mohr’s circle, determine the stresses acting on an element oriented at an angle θ from the x axis. Show these stresses on a sketch of an element oriented at the angle θ. (Note: The angle θ is positive when counterclockwise and negative when clockwise.) Given: σ_x=33 MPa,σ_y=-9 MPa,τ_xy=29 MPa,θ=35°

b oil d. water A vertical rectangular plate is submerged half in oil (SG = 0.83) and half in water as shown. Determine the ratio of force exerted by water to that of oil.