Question: A rectangular plate of side is submerged vertically in a fluid of density w, with its top edge at depth h. Show that if

A rectangular plate of side ℓ is submerged vertically in a fluid of density w, with its top edge at depth h. Show that if the depth is increased by an amount Δh, then the force on a side of the plate increases by wAΔh,where A is the area of the plate.

Step by Step Solution

★★★★★

3.22 Rating (149 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Let F be the force on a side of the plate when its top edge is at ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Calculus 4th Questions!

A vertical rectangular plate is submerged in a fluid with its top edge parallel to the fluids surface. Show that the force exerted by the fluid on one side of the plate equals the average value of...

A ball on a 1.50 m string is tied to a pole, 2.5 m above ground level. The ball is swung in a horizontal circle and the string breaks when the angle 8 (measured between the string and the vertical)...

Prove that the force on the side of a rectangular plate of area A submerged vertically in a fluid is equal to p 0 A, where p 0 is the fluid pressure at the center point of the rectangle.

Suppose that a plate is immersed vertically in a fluid with density and the width of the plate is w(x) at a depth of meters beneath the surface of the fluid. If the top of the plate is at depth a and...

Please answer the following questions using the examples as references. 1. Calculate the fluid force on one side of the plate using the coordinate system shown below. Assume the density is 62.4...

806 Chapter Fifteen OPTIMIZATION: LOCAL AND GLOBAL EXTREMA If f is not continuous or the region R is not closed and bounded, there is no guarantee that f achieves a global maximum or global minimum...

Consider the vertically submerged rectangular plate. We are going to determine the total force due to liquid pressure on the plate. The dimensions of the plate are W = 15 ft, L = 4 ft. The top of the...

Repeat Exercise 4, but assume that the top of the triangle is located 3 m below the surface of the water. Data From Exercise 4 A plate in the shape of an isosceles triangle with base 1 m and height 2...

Consider the vertically submerged rectangular plate. We are going to determine the total force due to liquid pressure on the plate. The dimensions of the plate are W = 12 ft, L = 8 ft . The top of...

A plate in the shape of an isosceles triangle with base 1 m and height 2 m is submerged vertically in a tank of water so that its vertex touches the surface of the water (Figure 7). (a) Show that the...

Rewrite the following function as a piecewise defined function: y(t) = 3sint - 2e-3u (t)e-3(t-1) + 2e-4u(t)e-2(t-2) After the rewrite: Answer: d sint + fe-3t + ge -2t y(t) = h sint + je-3t+ ke-2t (m...

When Steve divorced Laura, they agreed to split their assets equally. They had an account with an investment firm estimated to worth about $9.4 million. Steve paid Laura more than $6 million--...

The profit-maximizing condition for a competitive firm requires production to be carried to the point where marginal revenue is equal to marginal cost. Explain why. Is this condition the same for...

A new grocery store has 3 weeks to train its full staff of 39 employees. There are 5 employees now. At least 2 employees must work on preparing the store during the next week, 5 employees the week...

Without using a calculator, evaluate the following expressions or state that the quantity is undefined. sin -1 1

Without using a calculator, evaluate the following expressions or state that the quantity is undefined. cos -1 (-1)

Without using a calculator, evaluate the following expressions or state that the quantity is undefined. tan -1 1

What are three internal factors that enhance the probability of fraud, theft, and embezzlement? 2 paragraphs

You expect to receive $20,000 at graduation in two years. You plan on investing it at 9 percent until you have $98,000. How long will you wait from now? Multiple Choice 18.44 years 16.44 years 22.89...

Question 6 (of 6) value: 3.01 points Champion Contractors completed the following transactions and events involving the purchase and operation of equipment in its business. 2014 Jan. 1 Paid $322,000...