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In the process of changing a flat tire, a motorist uses a hydraulic jack. She begins by applying a force F1 = 5 N to the input piston. As a result, the output plunger applies a force of F2 = 340 N to the car. The height difference between the input piston and the output plunger can be neglected. What is the ratio A2/A1 of the plunger and piston areas?

In the process of changing a flat tire, a motorist uses a hydraulic jack. She begins by applying a force F1 = 5 N to the input piston. As a result, the output plunger applies a force of F2 = 340 N to the car. The height difference between the input piston and the output plunger can be neglected. What is the ratio A2/A1 of the plunger and piston areas?

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter15: Fluid Mechanics
Section: Chapter Questions
Problem 67P: A U-tube open at both ends is partially filled with water (Fig. P15.67a). Oil having a density 750...
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 In the process of changing a flat tire, a motorist uses a hydraulic jack. She begins by applying a force F1 = 5 N to

the input piston. As a result, the output plunger applies a force of F2 = 340 N to the car. The height difference

between the input piston and the output plunger can be neglected. What is the ratio A2/A1 of the plunger and

piston areas?

8:34 PM | 1.2KB/s ← اس. ه 4G+ 50 Pascal, Archimede... Pascal, Archimedes and Bernoulli Fluid Mechanics Seatwork 1. When a block (p = 6.00 x 10² kg/m³) is placed inside a container full of water, it floats partially and displaces 1.25 kg of water. (a) what is the volume of the block? (b) what is the bouyant force? 2. In the process of changing a flat tire, a motorist uses a hydraulic jack. She begins by applying a force F₁ = 5 N to the input piston. As a result, the output plunger applies a force of F₂ = 340 N to the car. The height difference between the input piston and the output plunger can be neglected. What is the ratio A₂/A₁ of the plunger and piston areas? 3. The figure at the right shows a tank that is open to the atmosphere at the top and has a pipe at the bottom, through which liquid exits. (a) Show that the expression for the speed of the liquid leaving the pipe is V₁ = √2gh (b) Calculate the speed v₁ of the liquid leaving the pipe if the difference in height is h = y₂ - Y₁ = 1.5 m. Hint: Assume that the liquid behaves as an ideal fluid (non-viscous). Therefore, we can apply Bernoulli's equation, and in preparation of doing so, we locate two points in the liquid. Point 1 is just outside the efflux pipe, and point 2 is at the top surface of the liquid. The pressure at each of these points is equal to the atmospheric pressure (P1 = P2 = atmospheric pressure), a fact that will be used to simplify Bernoulli's equation. Solution: (a) Show that the expression for the speed of the liquid leaving the pipe is v₁ = √2gh From the Bernoulli's equation 1 P₁ + pv² + pgy₁ = P₂ + pv² + pgy₂ 1 1 P₁ − P₂ + pv² + pgy₁ = =pv² + pgyz Since the pressures at points 1 and 2 are the same, P1 = P2, then P1 P2 = 0. 1 1 0+pv² +pgy₁ = ; =pv² +pgyz 1 1 pv² + pgy₁ = pv² +pgyz continue until you arrive at V₁ = √2gh Additional hint: h= y₂-y₁ and if the tank is very large, the liquid level changes only slowly, and the speed at point 2 can be set equal to zero (V₂ = 0). -
Transcribed Image Text:8:34 PM | 1.2KB/s ← اس. ه 4G+ 50 Pascal, Archimede... Pascal, Archimedes and Bernoulli Fluid Mechanics Seatwork 1. When a block (p = 6.00 x 10² kg/m³) is placed inside a container full of water, it floats partially and displaces 1.25 kg of water. (a) what is the volume of the block? (b) what is the bouyant force? 2. In the process of changing a flat tire, a motorist uses a hydraulic jack. She begins by applying a force F₁ = 5 N to the input piston. As a result, the output plunger applies a force of F₂ = 340 N to the car. The height difference between the input piston and the output plunger can be neglected. What is the ratio A₂/A₁ of the plunger and piston areas? 3. The figure at the right shows a tank that is open to the atmosphere at the top and has a pipe at the bottom, through which liquid exits. (a) Show that the expression for the speed of the liquid leaving the pipe is V₁ = √2gh (b) Calculate the speed v₁ of the liquid leaving the pipe if the difference in height is h = y₂ - Y₁ = 1.5 m. Hint: Assume that the liquid behaves as an ideal fluid (non-viscous). Therefore, we can apply Bernoulli's equation, and in preparation of doing so, we locate two points in the liquid. Point 1 is just outside the efflux pipe, and point 2 is at the top surface of the liquid. The pressure at each of these points is equal to the atmospheric pressure (P1 = P2 = atmospheric pressure), a fact that will be used to simplify Bernoulli's equation. Solution: (a) Show that the expression for the speed of the liquid leaving the pipe is v₁ = √2gh From the Bernoulli's equation 1 P₁ + pv² + pgy₁ = P₂ + pv² + pgy₂ 1 1 P₁ − P₂ + pv² + pgy₁ = =pv² + pgyz Since the pressures at points 1 and 2 are the same, P1 = P2, then P1 P2 = 0. 1 1 0+pv² +pgy₁ = ; =pv² +pgyz 1 1 pv² + pgy₁ = pv² +pgyz continue until you arrive at V₁ = √2gh Additional hint: h= y₂-y₁ and if the tank is very large, the liquid level changes only slowly, and the speed at point 2 can be set equal to zero (V₂ = 0). -
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