A thin plate moves between two parallel, horizontal, stationary flat surfaces at a constant velocity of $5 \mathrm{~m} / \mathrm{s}$. The two stationary surfaces are spaced $4 \mathrm{~cm}$ apart, and the medium between them is filled with oil whose viscosity is $0.9 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}^2$. The part of the plate immersed in oil at any given time is $2$-$\mathrm{m}$ long and $0.5$-$\mathrm{m}$ wide. If the plate moves through the mid-plane between the surfaces, find the force required to maintain this motion. What would your response be if the plate was $1 \mathrm{~cm}$ from the bottom surface $\left(h_2\right)$ and $3 \mathrm{~cm}$ from the top surface $\left(h_1\right)$ ?

Nitrogen enters a steady-flow heat exchanger at 150 kPa, $10^\circ C$, and 100 m/s, and it receives heat in the amount of 120 kJ/kg as it flows through it. Nitrogen leaves the heat exchanger at 100 kPa with a velocity of 200 m/s. Determine thejvlach number of the nitrogen at the inlet and the exit of the heat exchanger.

The density of seawater at a free surface where the pressure is 98 kPa is approximately $1030 kg/m^3.$ Taking the bulk modulus of elasticity of seawater to be $2.34 imes 109 N/m^2$ and expressing variation of pressure with depth as $dP= ho g\ dz$ determine the density and pressure at a depth of 2500 m. Disregard the effect of temperature.

A 0.018-in-diameter glass tube is inserted into mercury, which makes a contact angle of $140^{\circ}$ with glass. Find the capillary drop of mercury in the tube at $68^{\circ} \mathrm{F}$.

Reconsider the above problem. If the viscosity of the oil above the moving plate is $4$ times that of the oil below the plate, determine the distance of the plate from the bottom surface $\left(h_2\right)$ that will minimize the force needed to pull the plate between the two oils at constant velocity.

Determine the cm of a thin, uniform, semicircular plate, Fig. 9-61. [Hint: Integrate; see Problem 63.

Explain why a doctor would be worried about a child who broke a long bone close to the epiphyseal plate.

Find the center of mass of a plate that is shaped like the region between $y = x^2$ and $y = 2x$, where the density varies as $1 + x + y.$

The assembly shown in Figure P5.45 consists of a steel $\left[E_1=30,000 \mathrm{ksi} ; A_1=1.25 \mathrm{in}^2\right]$ rod (1), a rigid bearing plate $B$ that is securely fastened to rod (1), and a bronze $\left[E_2=15,000 \mathrm{ksi}\right.$; $A_2=3.75 \mathrm{in}^2{ }^2$ ] post (2). The yield strengths of the steel and bronze are $62 \mathrm{ksi}$ and $75 \mathrm{ksi}$, respectively. A clearance of $0.125 \mathrm{in}$. exists between the bearing plate $B$ and bronze post (2) before the assembly is loaded. After a load of $P=65$ kips is applied to the bearing plate, determine (a) the normal stresses in bars (1) and (2). (b) the factors of safety with respect to yield for each of the members. (c) the vertical displacement of bearing plate $B$.

Using the data given in Table, calculate the thickness of the quartz half-wave plate for $\lambda_0=5890 \text{\AA}$.

Under what conditions can the outer surface of a vertical cylinder be treated as a vertical plate in natural convection calculations?

A baseball diamond's home plate has three right angles. The other two angles are congruent. Find their measure.

If the energy stored by a $6 \mu \mathrm{F}$ capacitor is $1200 \mathrm{~J}$, find the charge $Q$ on each plate of the capacitor.

Two triangular plates are congruent. The area of one of the plates is 60 square inches.What is the area of the other plate? Explain.