Explore all our learning and teaching solutions

## Explore all our learning and teaching solutions

Got a Kanye-sized ego? → Test it on our Ego-Meter

### Sophia Pathways

Browse online college courses and customizable partnering solutions.

#### Institutions

High School Higher Education Corporate Learning

### Teach

Explore tools, news, technology and development resources for teachers.
• ##### Professional Learning Network
• Teachers’ Lounge Forum
• Our Teacher Blog
##### School of Thought

Insights & Ideas for Online Teaching

### Learn

Browse tutorials, test prep and other resources to improve academic skills and prepare for college.
+

# Fluid Force - Integral Calculation

&nbsp;
Actions
• Report
Embed
(15)
• (11)
• (1)
• (0)
• (1)
• (2)
##### Objective:

Students will be able to calculate fluid force on a vertical flat surface.

(more)
Tutorial

## Prerequisites

Students should be familiar with using definite integrals as summations.

## Fluid Force

This video develops the concept of using an integral to calculate the total fluid force on a vertical surface.

Source: self-created video

## Fluid Force Calculation Examples

This video walks through some examples of calculating fluid force.

Source: self-created video

## Problem Set

1. For each exercise, a vertical side of a tank is shaped as described. Calculate the fluid force on the side described. Assume the tank is filled to the top with water (62.4 lbs per cubic ft)

a. A rectangle of height 4 ft and width 5 ft (2496 lbs)

b. An isosceles trapezoid with parallel sides of length 3 ft and 4 ft. The parallel sides are horizontal and the shorter side is down. The distance between the parallel sides is 2 ft. (416 lbs)

c. The region bounded by and the x-axis (measurements in ft). (1064.96 lbs)

2.

a. A vertical circular porthole in an observation ship has diameter 1 ft. It is placed so that the center of the of the porthole is 2 ft below the surface of the ocean. Calculate the fluid force on the porthole (seawater: 64.0 lbs per cubic ft). (100.531 lbs)

b. What would be the fluid force on the same window if it was horizontal rather than vertical? (100.531 lbs)

3. One side of a form for poured concrete is the bottom half of the ellipse . Determine the fluid force on the plate when the form is filled, using 140.7 lbs per cubic ft for concrete. (1500.8 lbs)

4. A vertical plate is submerged in water (62.4). The plate is shaped as a square with length side 3 ft. The plate hangs from its corner and that top corner is 2 ft below the surface of the water. What is the fluid force on the plate? (2314.53 lbs)

5. A tanker truck is transporting gasoline (41 lbs per cubic ft) The tank is in the form of right cylinder with the round ends vertical. The radius of the tank is 3 ft and the distance between the bases is 15 ft. What is the fluid force on one end of the tank when it is full? (3477.74 lbs)

Paul’s Online Notes

Wolfram Alpha

## Where Do I Go From Here?

 PREVIOUS TUTORIAL NEXT TUTORIAL Definite Integrals Solid of Revolution - Shell Method

Sarah Hudak 9 months ago

Even when I do it in my calculator, the answer after the integrals is incorrect

Report
Sarah Hudak 9 months ago

On the second video with the trapezoid fluid pressure, it all makes sense, however when I do the math for the actual integral, I foiled it and integrated and do not get the same answer. I'm really confused and don't understand how I'm setting it up right but getting it wrong, still. I know it sounds dumb but can you please do the math out for the integrals?

Report
Rating

### No bones about it. Our Human Biology course is only \$329.

Sophia's online courses not only save you money, but credits are also eligible for transfer to over 2,000 colleges and universities.*