Problem 1: Horizontally Accelerating Tank without Spillage

An open tank is $3\text{ m}$ long and $2\text{ m}$ high and initially contains water to a depth of $1.5\text{ m}$. It accelerates horizontally at $2.5\text{ m/s}^2$. Determine the end depths, check for spilling, and find the maximum bottom gauge pressure.

Problem 2: Volume Spilled during Horizontal Acceleration

A tank is $4\text{ m}$ long, $2\text{ m}$ wide, and $2\text{ m}$ high. It initially contains water to a depth of $1.8\text{ m}$ and accelerates horizontally at $3.0\text{ m/s}^2$. Determine the spilled volume after relative equilibrium is reached.

Problem 3: Tank Accelerating Upward

A water tank accelerates vertically upward at $3.0\text{ m/s}^2$. Determine the gauge pressure $1.2\text{ m}$ below the free surface.

Problem 4: Tank Accelerating Downward

A water tank accelerates vertically downward at $6.0\text{ m/s}^2$. Determine the gauge pressure $1.5\text{ m}$ below the free surface and state the free-fall limit.

Problem 5: Combined Horizontal and Upward Acceleration

A $5\text{ m}$ long tank accelerates horizontally at $4.0\text{ m/s}^2$ while also accelerating upward at $2.0\text{ m/s}^2$. Determine the free-surface angle and end-to-end elevation difference.

Problem 6: Rotating Open Cylindrical Tank

A cylindrical tank is $1.2\text{ m}$ in diameter and $1.8\text{ m}$ high and initially contains water to a depth of $1.2\text{ m}$. It rotates at $60\text{ rpm}$. Determine the center and wall depths and check for spilling.

Problem 7: Speed for Incipient Spillage

An open cylindrical tank has radius $0.75\text{ m}$, height $1.50\text{ m}$, and initial water depth $1.00\text{ m}$. Determine the rotational speed at which water just reaches the rim.

Problem 8: Radial Pressure Difference in a Closed Rotating Tank

A completely filled cylindrical tank of water rotates at $8.0\text{ rad/s}$. Determine the pressure increase from the rotation axis to a point at radius $0.50\text{ m}$ at the same elevation.