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You have been asked to design a system that uses a single pump to move two pistons simultaneously. As shown in the figure, the system consists of two cylinders, A and B, connected by a pump. When the pump is operating at steady-state conditions, Piston A moves at 5 cm/s. Hydraulic Cylinder A Hydraulic Line Piston A Piston B Hydraulic Cylinder B Piston A has a diameter of 6 cm and Piston B has a diameter of 8 cm. The hydraulic line has a diameter of 2.5 cm. The hydraulic lines and cylinder walls are rigid. The hydraulic fluid is incompressible with a specific gravity of 0.8. (a) Starting with the conservation of mass equation and an open system of your choice, determine Pump i. the required volumetric flow rate into the pump in m³/s and gallons per minute (gpm) for Piston A to have the desired speed, and ii. the velocity of the hydraulic fluid at the pump inlet under these conditions. [Hint: Try a one-inlet/outlet open system with moving boundaries that contains the hydraulic fluid upstream of the pump.] (b) Starting with the conservation of mass equation and a closed system of your choice, determine the speed of Piston B when Piston A is moving at the desired value. [Hint: Try a deforming, closed system that includes all of the hydraulic fluid.] (c) Could you answer Part (b) using an open system? Briefly explain your answer but you need not do the analysis.

You have been asked to design a system that uses a single pump to move two pistons simultaneously. As shown in the figure, the system consists of two cylinders, A and B, connected by a pump. When the pump is operating at steady-state conditions, Piston A moves at 5 cm/s. Hydraulic Cylinder A Hydraulic Line Piston A Piston B Hydraulic Cylinder B Piston A has a diameter of 6 cm and Piston B has a diameter of 8 cm. The hydraulic line has a diameter of 2.5 cm. The hydraulic lines and cylinder walls are rigid. The hydraulic fluid is incompressible with a specific gravity of 0.8. (a) Starting with the conservation of mass equation and an open system of your choice, determine Pump i. the required volumetric flow rate into the pump in m³/s and gallons per minute (gpm) for Piston A to have the desired speed, and ii. the velocity of the hydraulic fluid at the pump inlet under these conditions. [Hint: Try a one-inlet/outlet open system with moving boundaries that contains the hydraulic fluid upstream of the pump.] (b) Starting with the conservation of mass equation and a closed system of your choice, determine the speed of Piston B when Piston A is moving at the desired value. [Hint: Try a deforming, closed system that includes all of the hydraulic fluid.] (c) Could you answer Part (b) using an open system? Briefly explain your answer but you need not do the analysis.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Problem 7.2 You have been asked to design a system that uses a single pump to move two pistons simultaneously. As shown in the figure, the system consists of two cylinders, A and B, connected by a pump. When the pump is operating at steady-state conditions, Piston A moves at 5 cm/s. Hydraulic Cylinder A Hydraulic Line Piston A Piston B Piston A has a diameter of 6 cm and Piston B has a diameter of 8 cm. The hydraulic line has a diameter of 2.5 cm. The hydraulic lines and cylinder walls are rigid. The hydraulic fluid is incompressible with a specific gravity of 0.8. (a) Starting with the conservation of mass equation and an open system of your choice, determine Hydraulic Cylinder B Pump i. the required volumetric flow rate into the pump in m³/s and gallons per minute (gpm) for Piston A to have the desired speed, and ii. the velocity of the hydraulic fluid at the pump inlet under these conditions. [Hint: Try a one-inlet/outlet open system with moving boundaries that contains the hydraulic fluid upstream of the pump.] cm (b) Starting with the conservation of mass equation and a closed system of your choice, determine the speed of Piston B when Piston A is moving at the desired value. [Hint: Try a deforming, closed system that includes all of the hydraulic fluid.] (c) Could you answer Part (b) using an open system? Briefly explain your answer but you need not do the analysis. Ans: i) 2.2 gpm ≤ ≤ 2.5 gpm ii) 25.1 ≤V ≤ 29.2cm/s
Transcribed Image Text:Problem 7.2 You have been asked to design a system that uses a single pump to move two pistons simultaneously. As shown in the figure, the system consists of two cylinders, A and B, connected by a pump. When the pump is operating at steady-state conditions, Piston A moves at 5 cm/s. Hydraulic Cylinder A Hydraulic Line Piston A Piston B Piston A has a diameter of 6 cm and Piston B has a diameter of 8 cm. The hydraulic line has a diameter of 2.5 cm. The hydraulic lines and cylinder walls are rigid. The hydraulic fluid is incompressible with a specific gravity of 0.8. (a) Starting with the conservation of mass equation and an open system of your choice, determine Hydraulic Cylinder B Pump i. the required volumetric flow rate into the pump in m³/s and gallons per minute (gpm) for Piston A to have the desired speed, and ii. the velocity of the hydraulic fluid at the pump inlet under these conditions. [Hint: Try a one-inlet/outlet open system with moving boundaries that contains the hydraulic fluid upstream of the pump.] cm (b) Starting with the conservation of mass equation and a closed system of your choice, determine the speed of Piston B when Piston A is moving at the desired value. [Hint: Try a deforming, closed system that includes all of the hydraulic fluid.] (c) Could you answer Part (b) using an open system? Briefly explain your answer but you need not do the analysis. Ans: i) 2.2 gpm ≤ ≤ 2.5 gpm ii) 25.1 ≤V ≤ 29.2cm/s
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