A plate having a thickness of $4.0 \mathrm{~mm}$ has an internal heat generation of $200 \mathrm{MW} / \mathrm{m}^3$ and a thermal conductivity of $25 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$. One side of the plate is insulated and the other side is maintained at $100^{\circ} \mathrm{C}$. Calculate the maximum temperature in the plate.

A carbon steel bar with diameter $=7.64$ in has a tensile strength of 65,000 $\mathrm{lb} / \mathrm{in}^2$ and a shear strength of $45,000 \mathrm{~lb} / \mathrm{in}^2$. The diameter is reduced in a turning operation at a cutting speed of $350 \mathrm{~ft} / \mathrm{min}$. Feed = $0.011 \mathrm{~in} / \mathrm{rev}$ and depth of cut $=0.120 \mathrm{~in}$. The rake angle on the tool in the direction of chip flow $=13^{\circ}$. The cutting conditions result in a chip ratio of 0.52. Using the orthogonal model as an approximation of turning, determine (a) shear plane angle, (b) shear force, (c) cutting force and feed force, and (d) coefficient of friction between the tool and chip.

What kinds of defects may exist in chilled white iron?

Water exits the 200-mm-diameter pipe at a velocity of 4 m / s and is split by the conical diffuser. Determine the force the flow exerts on the diffuser. Take $\theta=20^{\circ}$.

Water at $15^{\circ} \mathrm{C}$ flows through a nozzle that contracts from a diameter of $15 \mathrm{~cm}$ to $2 \mathrm{~cm}$. The exit speed is $v_2=10 \mathrm{~m} / \mathrm{s}$, and atmospheric pressure prevails at the exit of the jet. Estimate the pressure at section 1 and the force required to hold the nozzle stationary. Neglect weight.

The 100-mm-diameter pipe is used to transport crude oil at a temperature of $20^{\circ} \mathrm{C}$. Find the maximum allowable pressure drop if the flow is to be laminar over the $8$-m length of pipe.

A steel rotating-beam test specimen has an ultimate strength of 1600 MPa. Estimate the life of the specimen if it is tested at a completely reversed stress amplitude of 900 MPa.

The drum of mass $m$, radius $r$, and radius of gyration $k_G$ rolls along an inclined plane for which the coefficient of static friction is $\mu_x$. If the drum is released from rest, determine the maximum angle $\theta$ for the incline so that it rolls without slipping.

Liquid water is fed to a boiler at $24^{\circ} \mathrm{C}$ and 10 bar and is converted at constant pressure to saturated steam. (a) Use the steam tables to calculate $\Delta \hat{H}(\mathrm{kJ} / \mathrm{kg})$ for this process, and then determine the heat input required to produce $15,800 \mathrm{m}^{3} / \mathrm{h}$ of steam at the exit conditions. Assume the kinetic energy of the entering liquid is negligible and that steam is discharged through a 15-cm ID pipe. b) How would the calculated value of the heat input change if you did not neglect the kinetic energy of the inlet water and if the inner diameter of the steam discharge pipe were 13 cm (increase, decrease, stay the same, or no way to tell without more information)?

Heat is generated uniformly in a stainless steel plate having $k=20 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$. The thickness of the plate is $1.0 \mathrm{~cm}$ and the heat-generation rate is $500 \mathrm{MW} / \mathrm{m}^3$. If the two sides of the plate are maintained at 100 and $200^{\circ} \mathrm{C}$, respectively, calculate the temperature at the center of the plate.

The force F has a magnitude of 300 lb and acts along the diagonal of the parallelepiped as shown. Express F in terms of its magnitude times the appropriate unit vector and determine its x-, y -, and z-components.

The H-beam is subjected to a shear force of V=80 kN. Sketch the shear stress distribution acting along one of its side segments. Indicate all peak values.

The tank shown in Fig. is completely filled with water and accelerated. Calculate the maximum pressure in the tank if: (a) $a_x=20 \mathrm{~m} / \mathrm{s}^2, a_z=0, L=2 \mathrm{~m}$ (b) $a_x=0, a_z=20 \mathrm{~m} / \mathrm{s}^2, L=2 \mathrm{~m}$ (c) $a_x=60 ~\mathrm{ft} / \mathrm{sec}^2, a_z=60 ~\mathrm{ft} / \mathrm{sec}^2, L=6 ~\mathrm{ft}$ (d) $a_x=0, a_z=60 ~\mathrm{ft} / \mathrm{sec}^2, L=6 ~\mathrm{ft}$

The subway train shown is traveling at a speed of $30 \mathrm{mi} / \mathrm{h}$ when the brakes are fully applied on the wheels of cars $B$ and $C$, causing them to slide on the track, but are not applied on the wheels of car $A$. Knowing that the coefficient of kinetic friction is $0.35$ between the wheels and the track, determine $(a)$ the distance required to bring the train to a stop, $(b)$ the force in each coupling.