Fluid Mechanics and hydraulic lever

In summary, the conversation discusses an ideal hydraulic lever with two cylinders connected by a fluid-filled line. The output force is 100 times the input force and Pascal's principle states that pressure is evenly distributed. The question is how to find the output work, which may be simplified if simple machines only change the magnitude and direction of applied force.
  • #1
Qube
Gold Member
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1

Homework Statement


In a hydraulic lever consisting of two ideal fluid lined cylinder/pistons with a fluid filled line coupling the two cylinders, the output force is 100 times the input force. For 1 Joule of work done on the input side, the work done on the output side is (in J):

Homework Equations


AV=AV
Pressure is distributed evenly (Pascal's principle).

The Attempt at a Solution


I have no clue how to proceed.
This is what I had in mind.

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Last edited:
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  • #2
You question seems incomplete (and is missing combinations of the letters 'fl' for some reason). What are you trying to find?
 
  • #3
Oops, good point. I am trying to find the output work - the work done by the output cylinder.
 
  • #4
Is it true that simple machines do not change the amount of work done but only change the magnitude and/or the direction of the force applied? Because if so that makes this problem extremely easy.
 
  • #5


I can provide some insights on how fluid mechanics and hydraulic levers work to achieve a mechanical advantage. In this scenario, we have a hydraulic lever consisting of two ideal fluid lined cylinders with a fluid-filled line coupling them. This means that the fluid inside the cylinders and the connecting line is incompressible and able to transfer pressure evenly throughout the system.

Based on Pascal's principle, pressure is distributed evenly in a confined fluid. This means that the pressure exerted on one end of the fluid-filled line will be transmitted to the other end. In the case of our hydraulic lever, this means that the input force applied to one cylinder will be transmitted through the fluid to the other cylinder, resulting in a larger output force.

Now, let's consider the work done on each side of the lever. We know that work is equal to force multiplied by distance, or W = F x d. In this case, the distance traveled by the fluid is the same on both sides of the lever, as the cylinders and the connecting line are all of equal length. This means that the work done on each side is directly proportional to the force applied.

Since the input force is 100 times smaller than the output force, the work done on the input side will also be 100 times smaller than the work done on the output side. This means that for 1 Joule of work done on the input side, 100 Joules of work will be done on the output side. This is because the output force is 100 times larger than the input force, resulting in a 100-fold increase in work.

In summary, the hydraulic lever utilizes fluid mechanics to achieve a mechanical advantage, where a small input force can be amplified into a larger output force through the use of an incompressible fluid. The work done on each side of the lever is directly proportional to the force applied, resulting in a 100-fold increase in work for a 100-fold increase in force.
 

1. What is fluid mechanics?

Fluid mechanics is the branch of physics that deals with the study of fluids and their properties, including how they flow and interact with their surroundings.

2. What is a hydraulic lever?

A hydraulic lever is a simple machine that uses the pressure of a fluid, usually water or oil, to amplify force and perform work. It consists of two connected pistons of different sizes, with the smaller one exerting a larger force due to the pressure difference created by the fluid.

3. How does a hydraulic lever work?

A hydraulic lever works by using the principle of Pascal's law, which states that pressure exerted on a confined fluid is transmitted equally in all directions. When force is applied to the smaller piston, it creates a pressure that is transmitted through the fluid to the larger piston, causing it to move and exert a larger force.

4. What are the applications of fluid mechanics and hydraulic levers?

Fluid mechanics and hydraulic levers have a wide range of applications, including in engineering, transportation, and everyday appliances. They are used in hydraulic systems for heavy machinery, brakes in cars and airplanes, and even in simple tools like syringes and jacks.

5. What are the main principles of fluid mechanics?

The main principles of fluid mechanics include buoyancy, viscosity, continuity, and Bernoulli's principle. Buoyancy explains why objects float or sink in fluids, while viscosity describes a fluid's resistance to flow. Continuity relates to the conservation of mass in a fluid, and Bernoulli's principle states that as the speed of a fluid increases, its pressure decreases.

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