The tube rests on a $1.5$-$\mathrm{mm}$ thin film of oil having a viscosity of $\mu=0.0586 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}^2$. If the tube is rotating at a constant angular velocity of $\omega=4.5\ \mathrm{rad} / \mathrm{s}$, find the shear stress in the oil at $r=40 \mathrm{~mm}$ and $r=80 \mathrm{~mm}$. Assume the velocity profile within the oil is linear.

If the kinematic viscosity of glycerin is $v=1.15\left(10^{-3}\right) \mathrm{m}^2 / \mathrm{s}$, find its viscosity in FPS units. At the temperature considered, glycerin's specific gravity is $S_g=1.26$

The Newtonian fluid is confined between a plate and a fixed surface. If its velocity profile is defined by $u=\left(8 y-0.3 y^2\right) \mathrm{mm} / \mathrm{s}$, where $y$ is in $\mathrm{mm}$, find the shear stress that the fluid exerts on the plate and on the fixed surface. Assume $\mu=0.482 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}^2$.

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 $\left(h_1\right)$ ?

The Newtonian fluid is confined between the plate and a fixed surface. If its velocity profile is defined by $u=\left(8 y-0.3 y^2\right) \mathrm{mm} / \mathrm{s}$, where $y$ is in $\mathrm{mm}$, find the force $\mathbf{P}$ that must be applied to the plate to cause this motion. The plate has a surface area of $15\left(10^3\right) \mathrm{mm}^2$ in contact with the fluid. Assume $\mu=0.482 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}^2$.

A $50-cm imes 30-cm imes 20-cm$ block weighing 150 N is to be moved at a constant velocity of 0.80 m/s on an inclined surface with a friction coefficient of 0.27. (a) Determine the force F that needs to be applied in the horizontal direction. (b) If a 0.40-mm-thick oil film with a dynamic viscosity of $0.012 Pa\cdot s$ is applied between the block and inclined surface, determine the percent reduction in the required force.

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 viscosity of a fluid is to be measured by a viscometer constructed of two $75$-$\mathrm{cm}$-long concentric cylinders. The outer diameter of the inner cylinder is $15 \mathrm{~cm}$, and the gap between the two cylinders is $1 \mathrm{~mm}$. The inner cylinder is rotated at $300\ \mathrm{rpm}$, and the torque is measured to be $0.8 \mathrm{~N} \cdot \mathrm{m}$. Find the viscosity of the fluid.

Water in the swimming pool has a measured depth of $3.03 \mathrm{~m}$ when the temperature is $5^{\circ} \mathrm{C}$. Find its approximate depth when the temperature becomes $35^{\circ} \mathrm{C}$. Neglect losses due to evaporation.

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.

The tank contains air at a temperature of $18^{\circ} \mathrm{C}$ and an absolute pressure of $160 \mathrm{kPa}$. If the volume of the tank is $3.48 \mathrm{~m}^3$ and the temperature rises to $42^{\circ} \mathrm{C}$. Find the mass of air that must be removed from the tank to keep the same pressure.

Saturated water vapor at $150^\circ C$ (enthalpy h = 2745.9 kJ/kg) flows in a pipe at 50 m/s at an elevation of z = 10 m. Determine the total energy of vapor in J/kg relative to the ground level.

Find the weight of carbon tetrachloride that should be mixed with $15 \mathrm{\ lb}$ of glycerin so that the combined mixture has a density of $2.85\ \mathrm{slug} / \mathrm{ft}^3$.

A pump is used to transport water to a higher reservoir. If the water temperature is $20^\circ C$, determine the lowest pressure that can exist in the pump without cavitation.