Explanation Given information: The vertical cross section of a tank containing the mercury is given by Formula used: Suppose a flat surface is submerged vertically in a fluid of weight density δ and that the submerged portion of the plate extends from h = a to h = b on the vertical axis. Then the total force exerted by the fluid is given by of area A is submerged horizontally at a depth h in a fluid, the weight of the fluid exert a force called fluid force which is given by F = ∫ a b δ h L ( h ) d h Calculation: The weight density of mercury is 849.0 l b / f t 3 Consider the coordinate system in which the horizontal axis lies at the bottom of tank and the positive vertical axis points up. The centre point of the semicircle is ( 0 , 3 ) and its radius is 3. Therefore the equation for the line is x 2 + ( y − 3 ) 2 = 3 2 . ⇒ x = 9 − ( y − 3 ) 2 The thin slab has thickness Δ h and length L. Then, we have L = 2 x = 2 9 − ( y − 3 ) 2 The area of the slab is Δ A = L Δ h = 2 9 − ( y − 3 ) 2 Δ h The distance from the surface of the water to the x-axis is 2 ft

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J

Publisher: Kendall Hunt Publishing

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Differential Equations

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System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Chapter 6.5, Problem 26PS

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To find:The fluid force against the end of the vertical plate.

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Chapter 6.5, Problem 25PS

Chapter 6.5, Problem 27PS

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4. A hypodermic syringe contains a medicine with the density of water as shown in the figure. The barrel of the syringe has a cross- sectional area A = 2.50 × 10$ m², and the needle has a cross-sectional area a = 1.00 × 10* m² In the absence of a force on the plunger, the pressure everywhere is 1.00 atm. A force F of magnitude 2.00 N acts on the plunger, making medicine squirt horizontally from the needle. Determine the speed of the medicine as it leaves the needle's tip.

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10 7.7.009. MY NOTES ASK YOU Find the fluid force on the vertical side of the tank, where the dimensions are given in feet. Assume that the tank is full of water. (The weight-density of water is 62.4 pounds per cubic foot.) X lb Trapezoid 4 8. 2

Chapter 6 Solutions

Student's Solution and Survival Manual for Calculus

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The fluid force against the end of the vertical plate.

Solution Summary: The author calculates the fluid force against the end of a vertical plate. The horizontal axis lies at the bottom of the tank and the positive vertical axes points up.

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To find:The fluid force against the end of the vertical plate.

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Chapter 6 Solutions