# Thrust of Liquid

## What is meant by “Thrust of a liquid”?

Total force exerted on a surface in contact of a liquid mass is called thrust of liquid.

In equilibrium, a liquid exerts a force on any surface in contact with it. This force acts perpendicular to that surface.

• Thrust is a fundamental property of all liquids.
• Thrust exerted by a liquid is a force.

### Units of thrust

Thrust exerted by a liquid on a surface is the total force exerted normally on that surface. Hence, unit of thrust is similar to the unit of force.

• Hence, SI system unit of liquid thrust is newton.

## Fluid

A fluid is a substance that can flow and takes the shape of containing vessel because it cannot withstand shearing stress.

• Thus liquids and gases, both are fluids.

### Characteristics of fluids

Important characteristics of fluids are as follows –

1. The atoms or molecules of a fluid are arranged in a random manner.
2. A fluid cannot withstand tangential or shearing stress for a longer period. It begins to flow when a shearing stress is applied.
3. A fluid has no definite shape and size of its own. It ultimately assumes the shape of the containing vessel.
4. A fluid has no shear modulus or modulus of rigidity.
5. A fluid can exert a force in a direction perpendicular to its surface.
6. A liquid is an in-compressible fluid and has a definite volume and a free surface of its own.
7. A gas is a compressible fluid and it has no fixed volume. It expands to occupy all the space available in the container.

## Liquid

A liquid is an in-compressible fluid which has a fixed volume but its shape is not fixed and takes the shape of the container.

### Characteristics of liquids

A liquid has the following characteristics.

1. Liquid is a fluid which cannot withstand tangential or shearing stress for a longer period. It begins to flow when a shearing stress is applied.
2. A liquid is almost in-compressible fluid i.e. it is very difficult to reduce its volume by application of compressive stress.
3. Force of attraction between the atoms and molecules of liquid is less than that of solids but greater than that of gas. For this reason, the volume of a liquid is fixed like solids but its shape is not fixed. Volume and shape both of a gas are not fixed.
4. When a liquid is kept in a vessel, it exerts a force normal to the surface of the vessel. This force is called liquid thrust.

## Thrust & Pressure

The pressure at a point on a surface in contact with a liquid is the thrust acting normally per unit area around that point.

If, total force (thrust) ( F ) acts normally over a flat surface of area ( A ) then, the pressure is given by –

P = \left ( \frac {F}{A} \right )

If, the force is not uniform over the given surface then, pressure will be different at different points. If, a force ( \Delta F ) acts normally on a small area ( \Delta A ) surrounding a given point then pressure at that point will be –

P = \lim\limits_{\Delta A \rightarrow 0} \left ( \frac {\Delta F}{\Delta A} \right ) = \left ( \frac {dF}{dA} \right )

Pressure at a particular point in a fluid has same magnitude in all directions. This shows that a definite direction is not associated with fluid pressure. Hence, pressure is a scalar quantity.

• SI unit of pressure is ( \text {N-m}^{-2} ) \ \text {or Pascal}
• CGS unit of pressure is ( \text {dyne-cm}^{-2} )

### Importance of thrust & pressure

1. Area of sharp edge of a knife is much less than the area of blunt edge. Thus, for the same total force or thrust, the effective pressure in sharp knife is more than the blunt edge. Hence a sharp knife cuts better.
2. Wooden sleepers below the railway tracks spreads the force due to the weight of the train on a larger area and hence reduces the pressure on ground considerably.
3. A camel walks easily on sand because its feet have a larger area that make low pressure on sand.
4. Pins and nails are made with pointed ends to reduce the area which will produce greater pressure and facilitate penetration.

## Density

The density of any material is defined as its mass per unit volume.

If, a body of mass ( M ) occupies a volume of ( V ) , then its density is given by –

\text {Density} = \left ( \frac {\text {Mass}}{\text {Volume}} \right )

So, \quad \rho = \left ( \frac {M}{V} \right )

• Density is a scalar quantity.
• As liquids are in-compressible, so their density remains constant at all pressures. But density of a gas varies largely with pressure.
• The SI unit of density is ( \text {kg-m}^{-3} )
• The CGS unit of density is ( \text {g-cm}^{-3} )

### Specific gravity or Relative density

The specific gravity or relative density of a substance is defined as the ratio of the density of that substance to the density of water at ( 4 \degree C ) .

The density of water at ( 4 \degree C ) is ( 1.0 \times 10^3 \ \text {kg-m}^{-3} )

Therefore, \quad \text {Specific gravity} = \frac {\text {Density of substance}}{\text {Density of water at} 4 \degree \ C}

• Since, specific gravity is the ratio of two densities. It is a scalar quantity and it has no units.

Hence, \quad \text {Density of a substance} = \text {Specific gravity} \ \times \ \text {Density of water at} \ 4 \degree \ C

### Specific weight

As the specific gravity of a substance is defined as the ratio of the density of that substance to the density of water at ( 4 \degree C ) , in similar manner specific weight of a substance is defined as the ratio of the weight of that substance to the weight of same volume of water at ( 4 \degree C ) .

Therefore, \quad \text {Specific weight} = \frac {\text {Weight of unit volume of substance}}{ 4 \degree \ C \ \text {weight of unit volume of water}}

= \frac {\rho g}{1} ( Because, weight of unit volume of water is unit. )

= \rho g = \text {Density} \ \times \ \text {Acceleration due to gravity}

See numerical problems based on this article.