Question

A large storage tank, open at the top and filled with water, develops a small hole in its side at a point $16.0 \mathrm{m}$ below the water level. The rate of flow from the leak is found to be $2.50 \times 10^{-3} \mathrm{m}^{3} / \mathrm{min} .$ Determine (a) the speed at which the water leaves the hole and (b) the diameter of the hole.

Name: Problem 43, Chapter 15: Principles of Physics a Calculus Based Text
Uploaded: 2020-06-03T22:05:37-08:00
Duration: 3 min 6 s
Channel: Mayukh Banik
Description: A large storage tank, open at the top and filled with water, develops a small hole in its side at a point 16.0 m below the water level. The rate of flow from the leak is found to be 2.50 ×10^-3 m^3 / min . Determine (a) the speed at which the water leaves the hole and (b) the diameter of the hole.

   A large storage tank, open at the top and filled with water, develops a small hole in its side at a point $16.0 \mathrm{m}$ below the water level. The rate of flow from the leak is found to be $2.50 \times 10^{-3} \mathrm{m}^{3} / \mathrm{min} .$ Determine (a) the speed at which the water leaves the hole and (b) the diameter of the hole.

Principles of Physics a Calculus Based Text

Raymond A. Serway,… 5th Edition

Chapter 15, Problem 43

Instant Answer

Solved by Expert Mayukh Banik

06/03/2020

Step 1

We can use Bernoulli's equation to solve for the speed. Bernoulli's equation states that the sum of the pressure, kinetic energy per unit volume, and potential energy per unit volume is constant along a streamline. At the water surface, the pressure is Show more…

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A large storage tank, open at the top and filled with water, develops a small hole in its side at a point $16.0 \mathrm{m}$ below the water level. The rate of flow from the leak is found to be $2.50 \times 10^{-3} \mathrm{m}^{3} / \mathrm{min} .$ Determine (a) the speed at which the water leaves the hole and (b) the diameter of the hole.

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Key Concepts

Continuity Equation for Flow Rate

This concept relates the volumetric flow rate of fluid to the product of the cross-sectional area of an orifice and the velocity of the fluid exiting the orifice. It is expressed as Q = A × v. This relation is used to connect the measured flow rate with the theoretical velocity derived from Torricelli's law, enabling the determination of the size of the orifice or the exit velocity when one of the quantities is known.

Torricelli's Law

This principle states that the speed at which a liquid exits an orifice under gravity is equivalent to the speed acquired by a body falling freely through the same height. Mathematically, it is expressed as v = ?(2gh), where g is the acceleration due to gravity and h is the vertical distance from the free surface of the liquid to the orifice. This law is crucial in analyzing the problem of water flow from openings in containers.

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