Pascal's Law of Fluid Pressures Buoyancy & Archimedes' Principle Surface Tension

It was given by Swiss physicist

In the diagram , the same amount of fluid has to pass through the constriction during any given time as passes through the wider parts of the river, so

The same principle operates in the second diagram. During any given time interval the same volume has to pass through the narrow section A1 of the pipe with diameter 2h1 as through the wide section A2 (V1 = V2). Therefore the velocity v1 is larger than the velocity v2, and the pressure in the narrow part is smaller than in the wider part.

Consider tube of varying cross-section through which an ideal liquid is made to flow.

The mass m of the liquid crossing per second through any part of the tube is

or As a1 > a2

Therefore,

Now force on the liquid at section

And force on the liquid at section

Work done/second on the liquid at section

Work done/second by the liquid at section

Net work done/ second on the liquid by the pressure energy in moving the liquid from

section

When the mass m of the liquid flows in one second from A to B its height increases from h1 to h2 and its velocity increases from v1 to v2.

Therefore, increase in potential energy/second of the liquid from A to B =

Increase in kinetic energy /second of the liquid from A to B

According to work energy principle,

Dividing throughout by

so, we get:

Now,

Also called **Pascal's Principle**.

**Pascal's law** — developed by French mathematician** Blaise Pascal** — states that when there is an increase in
pressure at any point in a confined fluid,there is an equal increase at every other point in the container.

**Definition of Pressure:**
If F is the magnitude of the normal force on the piston and A is the surface area of a piston, then the pressure, P, of the
fluid at the level to which the device has been submerged as the ratio of the force to area.

**P = F / A**

Since the pressure is force per unit area, it has units of**N/m2** in the SI system.
Another name for the SI unit of pressure is **Pascal (Pa).**

**1 Pa = 1 N/m2**

An important application of Pascal's law is the**Hydraulic Press**.

A force F1 is applied to a small piston of area A1. The pressure is transmitted through a liquid to a larger piston of area A2. Since the pressure is the same on both sides, we see that P = F1/A1 = F2/A2. Therefore, the force F2 is larger than F1 by multiplying factor A2/A1.

**Hydraulic brakes,
car lifts, hydraulic jacks, and forklifts** all make use of this principle.

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## Buoyancy & Archimedes' Principle

Since the pressure is force per unit area, it has units of

An important application of Pascal's law is the

A force F1 is applied to a small piston of area A1. The pressure is transmitted through a liquid to a larger piston of area A2. Since the pressure is the same on both sides, we see that P = F1/A1 = F2/A2. Therefore, the force F2 is larger than F1 by multiplying factor A2/A1.

When a body is wholly or partially immersed in a fluid, the displaced fluid has a tendency to regain its original position, which exerts an upward force on the body. This upward force acting on the body immersed in a fluid is called

Archimedes’ principle

The

When W > W1

The body sinks in the fluid because of higher downward pull.

The body just floats or is at rest in the fluid.

The body floats comfortably.

The body floats because the weight of the liquid displaced by the immersed part of the body is at least equal to or greater than the weight of the body.

This phenomenon is valid with liquids only and not gasses.

** Surface tension** basically due to the **intermolecular attractions** in the liquid surface due to this a membrane effect can be seen on the surface.

**Or**

The **cohesive forces** between liquid molecules are responsible for the phenomenon
known as **surface tension**. The molecules at the surface do not have other like molecules on
all sides of them and consequently they cohere more strongly to those directly associated
with them on the surface. This forms a surface **"film"** which makes it more difficult to move
an object through the surface than to move it when it is completely submersed.

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