Fluid and Weight

Mass and Weight

Mass and weight are some of the common terms we come across in our everyday life. These terms are also confusing to many students new to physics. It is important to understand their meaning and how they differ with each other.
A mass of an object is the amount of matter contained by the object. The mass of an object does not change with location. For example, if the mass of an object is 10kg in earth, the object will have the same mass in moon.
The symbol for mass is m while the standard unit of measurement is kilogram.
Alternatively, weight of an object is the mass of the object acting upon by force of gravity. Since weight is a force, its standard unit of measure is in newton.
Just like mass that is independent of location, the weight of an object depends on the amount of force of gravity being acted upon the object. This implies that the weight of an object in earth will differ in moon since different amount of force of gravity acts on it.
The weight of an object is determined by multiplying the mass with acceleration of gravity.
W = m x a (N)
Another important phenomenon that is worth mentioning is weightlessness. Weightlessness is regarded as a state of free fall. Basically, the weight of an object depends on the mass and force of gravity which is supported by an object. If the supporting object is removed, weightlessness can be achieved.

Density and Relative Density

Density of an object was first discovered by a Greek scientist called Archimedes. It is simply a measurement of how compact the matter that made up the mass of an object is. If the matter is tightly held together the density of the object will be higher while the reverse is the case.
The density of an object can be obtained by using the mass of the object divided by the volume of the object.
Density = mass / volume (kg/m3)
The SI unit of density measurement is kg per cubic meter (kg/m3). Density can be found in use in many different areas in physics.
The symbol for density is the Greek letter rho, :
The relative density of an object is regarded as the ratio of the material’s density to the density of water. An object that has a density higher than density of water will sink in water where else an object will a lower density to that of water will float on water.

Pressure

Pressure is another important element in physics that deserve a thorough explanation – what it is and where it can be applied in real life.
Pressure can be defined as the measurement of a force per unit area. In its simple form, it is the force exerted by an object divided by the surface area on which the force is being acted upon.
It is important to understand the concept of pressure when two solids are involved and when pressure is applied in a fluid
For now let us just assume that we are dealing with two solids. In this situation, pressure can be calculated with the formula shown below.
Note: here that the force is applied perpendicular to the area
Pressure = Force / Area (Pascal)
The SI unit of pressure is called Pascal. The simple diagram below shows that pressure exerted on a solid surface.

Static Fluid Pressure

In a static fluid – a liquid or gas that is confirmed in a particular container, the pressure exerted by the fluid depends on the depth of the fluid, density of the fluid and the force of gravity.
Static fluid pressure = density x force of gravity x depth of fluid
The pressure in a liquid is exerted in all direction unlike in solid. The static fluid pressure does not depend on the shape, mass and surface area of the liquid.
The pressure at any point in a static fluid takes into consideration the pressure on top of the fluid and the depth of a particular spot on the liquid.
If two points are separated by a height (h) in a static fluid, there will be a high pressure in the lower point compare to the upper point.
The general equation to calculate the pressure in each depth in the fluid is shown below.
P2 = P1 + pgh

Pressure Using Pascal’s Principle

Another interesting concept of pressure is the work done by Pascal. Pascal’s principle stated that in a fluid that is completely enclosed in a system, a pressure applied at one point in the fluid will be transmitted to all other points in the fluid including the enclosing walls.
Pascal’s principle has found application in many equipment and measurement tools. A typical example is when you applied a pressure in a pipe containing liquid; the applied pressure is transmitted throughout the pipe.
Since the area in the container might not be the same so also the force being applied, the pressure will always remain the same. In other to find out the amount of force applied to the areas within the container, the following equation can be used.
P1 = P2 = F1 / A1 = F2 / A2

Pressure Measurement Using Barometer

Manometer is one of the instruments used to measure pressure. The mechanism by which the measurement occurs is by exploiting the relationship between pressure and depth. There are open-tube manometer and closed-tube manometer.
A typical example of a closed-tube manometer is a barometer. A simple diagram of a barometer is shown below.
A tube with one sealed end is filled with mercury and the open-end side of the tube is inserted into an open rectangle container that is filled with mercury. Since the top surface of the container is open, pressure is exerted by atmosphere pressure. The height from the surface of the container to the height of the mercury in the cylindrical pipe equals the pressure being measured.
The empty space at the end of the tube is at zero pressure. Note that this can only work if there is no air bubble present in the cylinder tube when placed inside the mercury container.

Equilibrium of Bodies

The equilibrium of bodies is a way to identify the forces acting on a body partially or completely immersed in a fluid. One scientist that came with a sound explanation about this concept is called Archimedes.
Archimedes’ principle stated that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces.
In a simple example, if an object of weight is dropped inside a cylinder container filled with water, if the weight of the water displaced is less than the weight of the object, the object will sink otherwise the object will float.
A diagram that illustrates Archimedes’ principle is shown below.