Problem 1: Density, Specific Weight, and Specific Gravity

A reservoir contains $825\text{ kg}$ of oil in a volume of $0.917\text{ m}^3$. Determine the oil density, specific weight, and specific gravity. Use $g=9.81\text{ m/s}^2$ and $\rho_w=1000\text{ kg/m}^3$.

Problem 2: Dynamic and Kinematic Viscosity

A lubricating oil has dynamic viscosity $\mu=0.290\text{ Pa}\cdot\text{s}$ and density $\rho=850\text{ kg/m}^3$. Determine its kinematic viscosity in $\text{m}^2/\text{s}$, stokes, and centistokes.

Problem 3: Viscous Force and Power between Parallel Plates

A plate of area $1.5\text{ m}^2$ moves at $0.4\text{ m/s}$ over a stationary plate. The plates are separated by a $0.15\text{ mm}$ layer of castor oil with $\mu=0.981\text{ Pa}\cdot\text{s}$. Assuming a linear velocity profile, determine the shear stress, resisting force, and required power.

Problem 4: Capillary Rise and Depression

A clean glass tube has inside diameter $2.5\text{ mm}$. Determine the capillary change when it is placed in (a) water with $\sigma=0.0725\text{ N/m}$ and $\theta=0^\circ$, and (b) mercury with $\sigma=0.52\text{ N/m}$, $SG=13.6$, and $\theta=130^\circ$.

Problem 5: Pressure inside a Droplet and a Soap Bubble

A water droplet and a soap bubble each have diameter $2.0\text{ mm}$. Take surface tension as $\sigma=0.072\text{ N/m}$. Calculate the excess internal pressure in each.

Problem 6: Determine Bulk Modulus from a Compression Test

A liquid volume decreases from $1000\text{ cm}^3$ at $1\text{ MPa}$ to $995\text{ cm}^3$ at $2\text{ MPa}$. Estimate its bulk modulus using the initial volume as the reference.

Problem 7: Volume Change from a Known Bulk Modulus

A rigid chamber initially contains $3.0\text{ m}^3$ of water. The pressure is increased by $5.0\text{ MPa}$. Estimate the decrease in volume using $K=2.2\text{ GPa}$.

Problem 8: Density and Specific Weight of Air

Air is at an absolute pressure of $150\text{ kPa}$ and a temperature of $30^\circ\text{C}$. Determine its density and specific weight using $R=287\text{ J/(kg}\cdot\text{K)}$.

Problem 9: Absolute Pressure and Cavitation Check

Water at $20^\circ\text{C}$ flows through a suction line where a gauge reads $-100.0\text{ kPa}$. Atmospheric pressure is $101.3\text{ kPa}$ and the water vapor pressure is $2.34\text{ kPa absolute}$. Determine the absolute pressure and assess cavitation risk.

Problem 10: Properties of a Two-Liquid Mixture

A tank receives $0.60\text{ m}^3$ of water with density $1000\text{ kg/m}^3$ and $0.40\text{ m}^3$ of oil with density $800\text{ kg/m}^3$. Assuming volumes are additive, determine the average mixture density, specific gravity, and specific weight.