Properties of Fluids: Worked Examples

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

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

A plate of area $1.50\ \text{m}^2$ moves at $0.400\ \text{m/s}$ over a stationary plate. A $0.150\ \text{mm}$ layer of castor oil separates them, with $\mu=0.981\ \text{Pa·s}$. Assuming steady Newtonian flow and a linear velocity profile, determine shear stress, resisting force, and required power.

A clean glass tube has inside diameter $2.50\ \text{mm}$. Determine the capillary change for (a) water with $\sigma=0.0725\ \text{N/m}$ and $\theta=0^\circ$, and (b) mercury with $\sigma=0.520\ \text{N/m}$, $SG=13.6$, and $\theta=130^\circ$. Use $\gamma_w=9810\ \text{N/m}^3$.

A water droplet and a soap bubble each have diameter $2.00\ \text{mm}$. Take $\sigma=0.0720\ \text{N/m}$. Determine the excess internal pressure in each.

A cylindrical water jet has diameter $4.00\ \text{mm}$ and surface tension $\sigma=0.0720\ \text{N/m}$. Neglecting axial curvature, determine the pressure inside the jet relative to the surrounding gas.

A liquid volume decreases from $1000\ \text{cm}^3$ at $1.00\ \text{MPa}$ to $995\ \text{cm}^3$ at $2.00\ \text{MPa}$. Estimate the average bulk modulus over this interval using the initial volume as the reference.

A chamber initially contains $3.00\ \text{m}^3$ of water. Pressure increases by $5.00\ \text{MPa}$. Estimate the volume decrease using $K=2.20\ \text{GPa}$ and treating $K$ as constant over the interval.

Air is at $150\ \text{kPa}$ absolute and $30.0^\circ\text{C}$. Determine density and specific weight using $R=287\ \text{J/(kg·K)}$ and $g=9.81\ \text{m/s}^2$.

Water at $20.0^\circ\text{C}$ flows through a suction line where a gage reads $-100.0\ \text{kPa}$. Local atmospheric pressure is $101.3\ \text{kPa}$ and water vapor pressure is $2.34\ \text{kPa}$ absolute. Determine the local absolute pressure and assess whether a single-phase liquid state is sustainable.

Air is at $200\ \text{kPa}$ absolute. Estimate its bulk modulus for (a) isothermal compression and (b) reversible adiabatic compression with $k=1.40$.