a) To find the width of triangle at depth y is f ( y ) = y 2 .

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Answer 1

Question

Chapter 9.3, Problem 4E

To determine

a)

To find the width of triangle at depth $y$ is $f (y) = \frac{y}{2} .$

To determine

b)

To find out the thin strip of thickness $Δ y$ at depth $y$ .Explain why the fluid force on a side of this strip is approximation equal to $ρ g \frac{1}{2} y^{2} Δ y$

To determine

c)

To find out an approximation for the total fluid force $F$ on a side of the plate as a Riemann sum and indicate the integral to which it converges.

To determine

d)

To calculate $F$ .

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A circular plate of radius r feet is submerged vertically in a tank of fluid that weighs w pounds per cubic foot. The center of the circle is k feet below the surface of the fluid, where k > r. Show that the fluid force on the surface of the plate is F = wk( r2 )

2. A dam has a triangular gate (triangle pointing upwards) with base 4 ft and height 5 ft. The top of the gate (the point of the triangle) is 3 feet below the water level. Set up an integral to find the fluid force on the gate. (The density of water is 62.4 lb/ft*.)

15. Figure 3 shows an object whose face is an equilateral triangle with 5-m sides. The object is 2 m thick and is submerged in water with its vertex 3 m below the water surface. Calculate the fluid force on both a triangular face and a slanted rectangular edge of the object. Water level 5 FIGURE 3

Answer 2

Question

Chapter 9.3, Problem 4E

To determine

a)

To find the width of triangle at depth $y$ is $f (y) = \frac{y}{2} .$

To determine

b)

To find out the thin strip of thickness $Δ y$ at depth $y$ .Explain why the fluid force on a side of this strip is approximation equal to $ρ g \frac{1}{2} y^{2} Δ y$

To determine

c)

To find out an approximation for the total fluid force $F$ on a side of the plate as a Riemann sum and indicate the integral to which it converges.

To determine

d)

To calculate $F$ .

Expert Solution & Answer

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Answer 3

Question

Chapter 9.3, Problem 4E

To determine

a)

To find the width of triangle at depth $y$ is $f (y) = \frac{y}{2} .$

To determine

b)

To find out the thin strip of thickness $Δ y$ at depth $y$ .Explain why the fluid force on a side of this strip is approximation equal to $ρ g \frac{1}{2} y^{2} Δ y$

To determine

c)

To find out an approximation for the total fluid force $F$ on a side of the plate as a Riemann sum and indicate the integral to which it converges.

To determine

d)

To calculate $F$ .

Expert Solution & Answer

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See solution

Answer 4

Question

Chapter 9.3, Problem 4E

To determine

a)

To find the width of triangle at depth $y$ is $f (y) = \frac{y}{2} .$

To determine

b)

To find out the thin strip of thickness $Δ y$ at depth $y$ .Explain why the fluid force on a side of this strip is approximation equal to $ρ g \frac{1}{2} y^{2} Δ y$

To determine

c)

To find out an approximation for the total fluid force $F$ on a side of the plate as a Riemann sum and indicate the integral to which it converges.

To determine

d)

To calculate $F$ .

Expert Solution & Answer

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Answer 5

Chapter 9.3, Problem 4E

To determine

a)

To find the width of triangle at depth $y$ is $f (y) = \frac{y}{2} .$

To determine

b)

To find out the thin strip of thickness $Δ y$ at depth $y$ .Explain why the fluid force on a side of this strip is approximation equal to $ρ g \frac{1}{2} y^{2} Δ y$

To determine

c)

To find out an approximation for the total fluid force $F$ on a side of the plate as a Riemann sum and indicate the integral to which it converges.

To determine

d)

To calculate $F$ .

Answer 6

Chapter 9.3, Problem 4E

To determine

a)

To find the width of triangle at depth $y$ is $f (y) = \frac{y}{2} .$

Answer 7

Chapter 9.3, Problem 4E

To determine

a)

To find the width of triangle at depth $y$ is $f (y) = \frac{y}{2} .$

Answer 8

To determine

b)

To find out the thin strip of thickness $Δ y$ at depth $y$ .Explain why the fluid force on a side of this strip is approximation equal to $ρ g \frac{1}{2} y^{2} Δ y$

Answer 9

To determine

b)

To find out the thin strip of thickness $Δ y$ at depth $y$ .Explain why the fluid force on a side of this strip is approximation equal to $ρ g \frac{1}{2} y^{2} Δ y$

Answer 10

To determine

c)

To find out an approximation for the total fluid force $F$ on a side of the plate as a Riemann sum and indicate the integral to which it converges.

Answer 11

To determine

c)

To find out an approximation for the total fluid force $F$ on a side of the plate as a Riemann sum and indicate the integral to which it converges.

Answer 12

To determine

d)

To calculate $F$ .

Answer 13

To determine

d)

To calculate $F$ .

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

Ch. 9.1 - Prob. 1PQ Ch. 9.1 - Prob. 2PQ Ch. 9.1 - Prob. 3PQ Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E

a) To find the width of triangle at depth y is f ( y ) = y 2 .

Solution Summary: The author explains that the solution obtained for y is f (y) = Y 2. Then, they determine an approximation for the total fluid force F on a side of the plate.

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a)

To find the width of triangle at depth $y$ is $f (y) = \frac{y}{2} .$

b)

To find out the thin strip of thickness $Δ y$ at depth $y$ .Explain why the fluid force on a side of this strip is approximation equal to $ρ g \frac{1}{2} y^{2} Δ y$

c)

To find out an approximation for the total fluid force $F$ on a side of the plate as a Riemann sum and indicate the integral to which it converges.

d)

To calculate $F$ .

Want to see the full answer?

Chapter 9 Solutions

a) To find the width of triangle at depth y is f ( y ) = y 2 .

Solution Summary: The author explains that the solution obtained for y is f (y) = Y 2. Then, they determine an approximation for the total fluid force F on a side of the plate.

Videos