The tank of water in Fig. P 2.142 is 12 cm wide into the...

The tank of water in Fig. $\mathrm{P} 2.142$ is $12 \mathrm{cm}$ wide into the paper. If the tank is accelerated to the right in rigid-body motion at $6.0 \mathrm{m} / \mathrm{s}^{2},$ compute $(a)$ the water depth on side $A B$ and $(b)$ the water-pressure force on panel $A B$. Assume no spilling.

The tank of water in Fig. $\mathrm{P} 2.142$ is $12 \mathrm{cm}$ wide into the paper. If the tank is accelerated to the right in rigid-body motion at $6.0 \mathrm{m} / \mathrm{s}^{2},$ compute
$(a)$ the water depth on side $A B$ and $(b)$ the water-pressure force on panel $A B$. Assume no spilling.

Key Concepts

Pressure Force on Submerged Surfaces

Calculating the force exerted by a fluid on a surface involves integrating the pressure distribution over the area of the surface. The pressure is not uniform due to the depth and acceleration effects, and determining the total force (and its point of application, the center of pressure) is essential in fluid mechanics.

Rigid-Body Motion in Fluids

This concept refers to a state where the entire fluid moves together as a single unit under external acceleration, without relative motion between different parts of the fluid aside from adjustments in the free surface. It simplifies analysis by allowing the use of hydrostatic principles in a noninertial reference frame.

Hydrostatic Pressure in Accelerated Systems

This concept involves understanding how pressure in a fluid at rest (or in steady motion) is affected when the system accelerates. In an accelerating frame, the effective gravitational field is the vector sum of the usual gravitational acceleration and the acceleration of the system, leading to a modified pressure distribution.

Free Surface Inclination

In an accelerating fluid, the free surface adjusts to be perpendicular to the effective gravitational field. This inclination is a result of the balance between gravitational forces and inertial (acceleration) forces, and it is key to determining the depth variations along the container walls.

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