Pressure and Force in Fluid Dynamics: Clarifying the Application of Pascal's Law

In summary, the conversation discusses Pascal's law and its application to a horizontal tube with different areas. It is stated that according to the law, if a force of 100N is exerted on one side with an area of 10m2, the pressure within the fluid will also be 10Pa. The OP asks if this means the fluid will keep moving towards the direction of smaller area indefinitely. They also question the pressure and direction of movement if a force of 11N is exerted on the 1m2 side while the 100N force is still present. The conversation concludes with a mention of the need to consider the Bernoulli equation and the effect of viscous frictional pressure drop.
  • #1
noobie_doobie
3
0
Appreciate all assistance in clearing my flow of thoughts with regards to the topic on Pascal Law...

Scenario : A horizontal tube (consisting of fluid) having an area of 10m2 and 1m2 on opposite side
If I were to exert a force of 100N on one side of a surface of 10m2(pressure will then be 10Pa), according to Pascal law, the pressure within the fluid will be 10Pa. Consequently, at the 1m2 side i will only be able to push overcome a resistance of 10N.
Does this means that since there is an inbalance of forces(100N vs 10N), the fluid will keep moving towards the direction of smaller area indefinitely if the condition remain??

My confusion arise here : Say if I to exert a force of 11N on the 1m2 side, with the force of 100N still acting on the 10m2 surface, what will the pressure inside the liquid be(10Pa or 11Pa). Also, in which direction will the fluid move??

Thanks!
 
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  • #2
The OP should be analyzing this using the Bernoulli equation. Also, no consideration is given to viscous frictional pressure drop.
 

What is Pascal's Law?

Pascal's Law, also known as the principle of transmission of fluid-pressure, states that pressure applied to a confined fluid is transmitted equally in all directions without any loss. This means that if pressure is applied to one part of a fluid, it will be equally distributed throughout the entire fluid and to the walls of the container.

What is the relationship between force and pressure according to Pascal's Law?

According to Pascal's Law, the pressure in a fluid is directly proportional to the force applied and the area over which it is distributed. This means that as the force increases, the pressure also increases, and vice versa. This relationship is expressed as P = F/A, where P is pressure, F is force, and A is the area over which the force is applied.

How is Pascal's Law applied in everyday life?

Pascal's Law is applied in many everyday situations, such as hydraulic systems used in cars and construction equipment. It is also the principle behind the functioning of hydraulic lifts and jacks, which use a small force over a small area to lift a heavier object over a larger area.

What are some limitations of Pascal's Law?

Pascal's Law is based on the assumption that the fluid is incompressible and the container is rigid. In reality, there is always some degree of compression in a fluid, and containers can deform under high pressures. Additionally, Pascal's Law does not take into account the effects of gravity, surface tension, and viscosity, which can also affect the distribution of pressure in a fluid.

How important is Pascal's Law in the field of fluid mechanics?

Pascal's Law is a fundamental principle in the study of fluid mechanics and is used to understand and predict the behavior of fluids in various systems. It is also essential in the design and operation of hydraulic and pneumatic systems, which are widely used in industries such as manufacturing, transportation, and construction.

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