A 20 - ft -long, 8 - ft -high rectangular tank open to the...

Name: Problem 55, Chapter 11: Fundamentals of Thermal-Fluid Sciences
Uploaded: 2022-04-13T19:14:25-08:00
Duration: 2 min 31 s
Channel: Kudakwashe Mapiki
Description: A 20 - ft -long, 8 - ft -high rectangular tank open to the atmosphere is towed by a truck on a level road. The tank is filled with water to a depth of 6 ft . Determine the maximum acceleration or deceleration allowed if no water is to spill during towing.

A 20 - ft -long, 8 - ft -high rectangular tank open to the atmosphere is towed by a truck on a level road. The tank is filled with water to a depth of 6 ft . Determine the maximum acceleration or deceleration allowed if no water is to spill during towing.

Key Concepts

Free Surface Effect

The free surface effect refers to the tendency of the surface of a fluid to adjust its orientation in response to acceleration. In an accelerating vehicle, the water’s surface becomes inclined, making one side higher and the other lower. This effect must be carefully considered in applications such as fuel tanks or towing water tanks because it can lead to spillage if the tilt causes the fluid to reach or exceed the container’s boundaries.

Geometric Constraints for Preventing Spillage

This concept involves determining the limits of acceleration by analyzing the geometry of the container and the level of the fluid within it. By relating the tilt angle of the free surface to the dimensions of the container (such as the height and length) and the initial fluid depth, one can derive the maximum permissible acceleration (or deceleration) that prevents the fluid from reaching the top edge of the container and spilling over.

Fluid Statics in Accelerated Frames

This concept deals with the behavior of a fluid when the container (or the reference frame) is accelerating. In such a scenario, the free surface of the fluid tilts so that it remains perpendicular to the net acceleration vector, which is the vector sum of gravitational acceleration and the acceleration of the frame. This tilt explains how the fluid redistributes itself under acceleration, a key principle in analyzing spillage in moving containers.

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