Consider two identical glasses of water, one stationary and...

Name: Problem 40, Chapter 11: Fundamentals of Thermal-Fluid Sciences
Uploaded: 2020-02-16T18:32:38-08:00
Duration: 3 min 52 s
Channel: Alexander Allen
Description: Consider two identical glasses of water, one stationary and the other moving on a horizontal plane with constant acceleration. Assuming no splashing or spilling occurs, which glass will have a higher pressure at the (a) front, (b) midpoint, and (c) back of the bottom surface?

Consider two identical glasses of water, one stationary and the other moving on a horizontal plane with constant acceleration. Assuming no splashing or spilling occurs, which glass will have a higher pressure at the (a) front, (b) midpoint, and (c) back of the bottom surface?

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Key Concepts

Hydrostatic Pressure

This concept refers to the pressure in a fluid at rest due to the weight of the fluid above a given point. In a stationary container, the pressure increases uniformly with depth because of the gravitational force acting on the water. The relationship is determined by the fluid density, gravitational acceleration, and the depth of the fluid column above the point of interest.

Non-Inertial Reference Frames and Fictitious Forces

When a container of fluid is accelerating, the analysis of pressure distribution must be done in a non-inertial reference frame, which involves introducing fictitious forces. These forces appear to act on the fluid in the opposite direction to the acceleration and modify the effective gravitational field experienced by the fluid. This change affects how the pressure varies across the container's base.

Free Surface Tilt in Accelerated Fluids

Under constant acceleration, the free surface of a fluid reaches a new equilibrium state where it tilts to balance the real gravitational force and the fictitious inertial force. The surface tilts such that its normal is aligned with the net effective gravitational field. This tilt means that the depth of the fluid varies from the front to the back of the container, leading to a non-uniform pressure distribution along the base.

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