Find out the hydrostatic force on the triangular plate, Mathematics

Assignment Help:

Find out the hydrostatic force on the following triangular plate that is submerged in water as displayed.

971_Find out the hydrostatic force on the triangular plate 5.png

Solution

The first thing to do here is set up an axis system.  Thus, let's redo the diagram above with the following axis system added in.

2306_Find out the hydrostatic force on the triangular plate 4.png

Thus, we are going to orient the x-axis that is why positive x is downward, x = 0 corresponds to the water surface and x = 4 refers to the depth of the tip of the triangle. After that we break up the triangle into n horizontal strips every equal width Δx and in each interval [xi-1,xi] select any point xi* .

To make the computations easier we are going to make two assumptions about these strips. First, we will ignore the fact that in fact the ends are going to be slanted and presume the strips are rectangular. If Δx is adequately small this will not affect our computations much.

Second, we will assume that Δx is small enough that the hydrostatic pressure on every strip is necessarily constant. Below is a representative strip.

463_Find out the hydrostatic force on the triangular plate 3.png

The height of this strip is Δx and the width is 2a.  We can use identical triangles to determine a as follows,

¾ = a / 4-xi*

= a 3- ¾ xi*

Here now, as we are assuming the pressure on this strip is constant, the pressure is illustrated by,

Pi = ρgd = 1000 (9.81) xi*

= 9810 xi*

and the hydrostatic force on every strip is,

Fi = Pi A = Pi (2aΔx)

= 9810 xi* (2) (3- (3/4) xi*)Δx

=19620 xi* (3- (3/4) xi*)Δx

The estimated hydrostatic force on the plate is then the sum of the forces on all the strips or,

424_Find out the hydrostatic force on the triangular plate 2.png

Taking the limit will obtain the exact hydrostatic force,

593_Find out the hydrostatic force on the triangular plate 1.png

By using the definition of the definite integral this is nothing much more than,

F = ∫40 19620 (3x - ¾ x2) dx

The hydrostatic force is then

F = ∫40 19620 (3x - ¾ x2) dx

= 19620 (3/2 x2 - ¼ x3) |40

= 156960 N


Related Discussions:- Find out the hydrostatic force on the triangular plate

Theory of equations, If p,q,r are roots of x^3-3x^2+4x-7=0 (p+2)(q+2)(...

If p,q,r are roots of x^3-3x^2+4x-7=0 (p+2)(q+2)(r+2)=

What it means to count-learning to count, What do we understand by "being a...

What do we understand by "being able to count"? Think about the following situation before you answer. Example 1: Three year-old Mini could recite numbers from I to 20 in the co

Equation, how to slove problems on equations

how to slove problems on equations

How many gumdrops, Will has a bag of gumdrops. If he eats 2 of his gumdrops...

Will has a bag of gumdrops. If he eats 2 of his gumdrops, he will have among 2 and 6 of them left. Which of the subsequent represents how many gumdrops, x, were originally in his b

Stakeholders, what is the benefit for stakeholders or disadvantage in a mon...

what is the benefit for stakeholders or disadvantage in a monoply

Least common denominator, Let's recall how do to do this with a rapid numbe...

Let's recall how do to do this with a rapid number example.                                                     5/6 - 3/4 In this case we required a common denominator & reme

Potency of a drug , An experiment designed to test the potency of a drug on...

An experiment designed to test the potency of a drug on 20 rats. Last animal studies have shown that a 10 mg dose of the drug is lethal 5% of the time within the first 4 hours; of

Determine the numbers of sides in regular polygon, If each interior angle o...

If each interior angle of a regular polygon has a calculated as of 144 degrees, Determine the numbers of sides does it have? a. 8 b. 9 c. 10 d. 11   c. The measur

The width of a rectangle is 30.5% of its length, The width of a rectangle i...

The width of a rectangle is 30.5% of its length l. Write a formula for the area and perimeter of the rectangle in terms of l only

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd