h2 42 х μι Fixed

A cylindrical tank shown below has a radius ? and a circular orifice at the bottom of radius ?. At time ? = 0 the liquid level in the tank is ho. (a) Use the Bernoulli equation to determine the relations between the orifice velocity ?o and the free surface velocity ?s (assume the surface velocity is not zero). (b) Use conservation of mass to determine the orifice velocity in terms of the free surface velocity. (c) Use the results in (a) and (b) to derive a differential equation for h(?). Note that ?s = − dh/dt. d) Separate variables and solve the equation for h(?) with the initial condition h(0) = ho (e) Determine how long it will take to empty the tank.

An isothermal long cylinder with square (side of 0.4 m and diagonal of 0.5657 m) cross-section is placed in a flow with a velocity of 1 m/s as shown. The properties of the fluid are: kinematic viscosity is 1.38 x 10-5 m²/s, thermal conductivity is 0.024 W/m.°C, and Prandtl number is 0.73. What is the average Nusselt number for the flow? 1253 a Figure 1: Flow configuration for Problem 6. The dimensions are: a=0.4 m, b=0.5657 m

A 1-in-diameter (D = 1 inch) rotating machined shaft has a groove 0.1-in deep with a 0.1-in radius machined into it. The shaft is subjected to a pulsating (i.e. R = 0) torque and bending moment of following values. Based on laboratory experiments at 550°F, Sut = 150 ksi, Sy = 120 ksi, and S'e = 90 ksi are measured. Using mod-Goodman equation and for operating temperature of 550°F and 90% reliability, determine the factor of safety for yielding and fatigue of this shaft. Tmax = 2000 Ib-in Mmax = 1600 lb-in Mmin = -1200 Ib-in D - -d- M T M T