À vertical cylindrical tank of height h and radius R has a narrow crack of width w running vertically from top to bottom. If the tank is initially filled with water and allowed to drain through the crack under the influence of gravity, find the instantaneous depth of the water as a function of time. How long will it take the tank to empty? Hint: First imagine the crack to be a series of adjacent orifices, anc integrate to find the total efflux from the crack in the infinites imal time interval dt. 3:43

À vertical cylindrical tank of height h and radius R has a narrow crack of width w running vertically from top to bottom. If the tank is initially filled with water and allowed to drain through the crack under the influence of gravity, find the instantaneous depth of the water as a function of time. How long will it take the tank to empty? Hint: First imagine the crack to be a series of adjacent orifices, anc integrate to find the total efflux from the crack in the infinites imal time interval dt. 3:43

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Description: A vertical cylindrical tank of heighth and radius R has a narrow crackof width w running vertically fromtop to bottom. If the tank is initiallyfilled with water and allowed to drainthrough the crack under the influenceof gravity, find the instantane

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Fluid Pressure

The term fluid pressure is coined as, the measurement of the force per unit area of a given surface of a closed container. It is a branch of physics that helps to study the properties of fluid under various conditions of force.

Gauge Pressure

Pressure is the physical force acting per unit area on a body; the applied force is perpendicular to the surface of the object per unit area. The air around us at sea level exerts a pressure (atmospheric pressure) of about 14.7 psi but this doesn’t seem to bother anyone as the bodily fluids are constantly pushing outwards with the same force but if one swims down into the ocean a few feet below the surface one can notice the difference, there is increased pressure on the eardrum, this is due to an increase in hydrostatic pressure.

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Question

A vertical cylindrical tank of height
h and radius R has a narrow crack
of width w running vertically from
top to bottom. If the tank is initially
filled with water and allowed to drain
through the crack under the influence
of gravity, find the instantaneous
depth of the water as a function of
time. How long will it take the tank to
empty? Hint: First imagine the crack
to be a series of adjacent orifices, and
integrate to find the total efflux from
the crack in the infinites imal time
interval dt.
P 3:43

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