Answered: Gate У1 У2 V2

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

In Fig. let y₁ = 6 ft and the gate width b= 8 ft.
Find the gate opening H that would allow a free-discharge
fl ow of 30,000 gal/min under the gate.

Expert Solution

Step 1

Given data

$\begin{array}{rcl} y_{1} & = & 6 ft \\ b & = & 8 ft \\ Q & = & 30000 gal / \min \\ = & 66.84 {ft}^{3} / s \end{array}$

Step 2

The discharge is given by the following expression:

$Q = \frac{0.61}{\sqrt{1 + 0.61 H / y_{1}}} H b \sqrt{2 g y_{1}}$

Substitute the necessary values in above equation

$66.84 {ft}^{3} / \sec = [\frac{0.61}{\sqrt{1 + 0.61 H / (6 ft)}}] (H) (6 ft) \sqrt{2 (32.2 ft / s^{2}) (6 ft)}$

By solving the above expression

$H = 0.72 ft$

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