   Chapter 8.3, Problem 4E

Chapter
Section
Textbook Problem

A vertical plate is submerged (or partially submerged) in water and has the indicated shape. Explain how to approximate the hydrostatic force against one side of the plate by a Riemann sum. Then express the force as an integral and evaluate it.4. To determine

To express: The hydrostatic force as an integral function using the Riemann sum.

To evaluate: the integral as the function of hydrostatic force.

Explanation

Given:

The height of the vertical triangle plate is 5 ft.

The width of the vertical triangle plate is 10 ft.

The vertical triangle plate is submerged in the depth of the water is 7 ft.

Calculation:

Consider the weight density of water is δ=62.5lb/ft3 .

Draw the vertical triangle plate x-axis as shown in Figure 1.

Refer to Figure 1.

Calculate the width of the ith strip as follows:

wixi2=105wi=2(xi2)

The depth of the ith strip as follows:

di=xi

Calculate the area of the ith rectangular strip using the Riemann sum:

Ai=wiΔx (1)

Substitute 2(xi2) for wi in Equation (1).

Ai=2(xi2)Δx

Calculate the pressure of the ith strip using the Riemann sum:

Pi=δdi (2)

Substitute xi for di in Equation (2).

Pi=δxi

The hydrostatic force as an integral using the Riemann sum:

F=limni=1nPiAi (3)

Substitute δxi for P and 2(xi2)Δx for A in Equation (3)

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Prove the statement using the , definition of a limit. limx2(x24x+5)=1

Single Variable Calculus: Early Transcendentals, Volume I

Given: m9=2x+17m11=5x94 Find: x

Elementary Geometry For College Students, 7e

Use a Table of Integrals to evaluate .

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Explain the difference between passive and active deception.

Research Methods for the Behavioral Sciences (MindTap Course List) 