Worksheet - Fire Suppression System

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Kent State University *

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35040

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Mechanical Engineering

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Dec 6, 2023

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docx

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6

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Name:___ AERN 45030 – Aircraft Systems II Worksheet Lesson Two – Fire Suppression Systems DUE: 16 Feb - Beginning of class ___________________________________________________________________________________ This worksheet is designed to exercise both basic laws of physics while focusing on Pascal’s Law to better understand the methods behind the hydraulic/pneumatic design implementations considered within an aircraft’s fire suppression system. The exam will use variations of these formulas and relationship to exercise your knowledge. All diagrams and formulas WILL be provided on the exam as shown here. Complete/answer the following questions/problems. Calculate to the nearest hundredth (.00), show your work and make sure you provide the proper unit(s) with your work. Circle your answer. Formulas for finding area: Formulas for finding volume:
Relationship between Relationship between Force/pressure/area volume/area/distance Mechanical Advantage Use the formulas/relationship listed on the previous page to calculate the following: 1. Find the area of a circle with a 10 inch diameter:
2. Find the volume of a cylinder 8 inches high with a diameter of 6 inches: 3. How much force will a 1000 psi hydraulic system, acting on a piston with an area of 0.5 square inch produce? 4. The area needed for a 1000 psi hydraulic system to produce a force of 5000 pounds is? 5. How much pressure is needed to act on a piston with an area of 2 square inches to produce 5000 pounds of force? 6. How much fluid will be displaced when a piston with an area of 20 square inches is moved into a cylinder for a distance of 5 inches? 7. What area must a piston have to move 100 cubic inches of fluid from a cylinder with a piston movement of 5 inches? 8. How far must a 20 square inch piston move to displace 100 cubic inches of fluid? The formulas that relate to the following problems are shown below: P1 = P2 (since the pressures are equal throughout). Since pressure equals force per unit area, then it follows that
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F1/A1 = F2/A2 It can be shown by substitution that the values shown above are correct, 1 pound / 1 square inches = 10 pounds / 10 square inches Because the volume of fluid pushed down on the left side equals the volume of fluid that is lifted up on the right side, the following formula is also true. V1 = V2 by substitution, A1 D1 = A2 D2 A = cross sectional area D = the distance moved or A1/A2= D2/D1 This system can be thought of as a simple machine (lever), since force is multiplied. The mechanical advantage can be found by rearranging terms in the above equation to Mechanical Advantage (IMA) MA = D1/D2 = A2/A1 MA = FR (Output) / FE (Input) For the sample problem above, the IMA would be 10:1 (10 inches/ 1 inch or 10 square inches / 1 square inch). Given these formulas, answer the following questions: 9. A hydraulic press has an input cylinder 1 inch in diameter and an output cylinder 6 inches in diameter. a. Assuming 100% efficiency, find the force exerted by the output piston when a force of 10 pounds is applied to the input piston.
b. If the input piston is moved through 4 inches, how far is the output piston moved? 10. A hydraulic system is said to have a mechanical advantage of 40. Mechanical advantage (MA) is: FR (output) / FE (input). If the input piston, with a 12 inch radius, has a force of 65 pounds pushing downward a distance of 20 inches, find: a. The volume of fluid that has been displaced
b. The upward force on the output piston c. The radius of the output piston d. The distance the output piston moves
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