In engineering, the concepts of pressure, drop in pressure, force, work, and the laws of gases are basic in any design or analysis when participation of a system containing either a fluid or a gas is involved. This is primarily because the fluids or gases are usually the ones in motion through the system under use.The elaboration of each one of them has been done in the following article, considering their interrelation with each other with respect to the flow of fluids through a pipeline or the behavior of a gas.
1. Pressure: This is the force per unit area that acts on an object's surface. The pressure in a surface measures how strong a force is applied normal, or perpendicular to the surface.
P = F/A
where,
P=pressure,
F=force applied,
A=area of distribution,
P=pressure,
F=force applied,
A=area of distribution,
Pressure SI unit is Pascal (Pa), where 1 Pa=1N/m2
Other units of pressure which are in common use are: atmospheres (atm), bar and psi (pounds per square inch).
Other units of pressure which are in common use are: atmospheres (atm), bar and psi (pounds per square inch).
2. Pressure Drop: The pressure loss from one point to another in a fluid system is termed as pressure drop. This effect is quite vital during the designing of pipelines, amongst other fluid transportation systems. In general, the frictional losses in a pipe, reduction/increment in pipe diameter and other bends, valves, and fittings bring about pressure drop.
where,
ΔP = pressure drop,
f = Darcy friction factor,
L is the length of pipe,
D is the diameter of the pipe,
ρ is the fluid density,
v is the flow velocity.
ΔP = pressure drop,
f = Darcy friction factor,
L is the length of pipe,
D is the diameter of the pipe,
ρ is the fluid density,
v is the flow velocity.
3. Force: It is a vector quantity which causes an object to accelerate. It is an interaction which, if unopposed, changes the motion of an object.
F = ma
where:
F is the force,
m is the mass of the object,
a is the acceleration.
F is the force,
m is the mass of the object,
a is the acceleration.
4. Work: Work is said to be done when a force acts upon an object to move it some distance. It is a measure of energy transfer.
where,
W = work done,
F = force,
d = distance moved,
θ = angle between the force and direction of movement.
F = force,
d = distance moved,
θ = angle between the force and direction of movement.
5. Flow Through Pipelines: The flow of fluids or gases through pipes, in general, is termed flow through pipelines in engineering. Factors that may affect the nature of flow are related to pipe diameter, the length of the pipe, roughness, properties of the fluid, and also pressure gradient.
a. Continuity Equation: The equation that provides that in the flow of a fluid the mass is conserved. That is, it says in effect that the mass flow rate is constant from point to point in a pipe: For incompressible fluids (those that are not readily compressible such as liquids and also gases under certain conditions):
where:
A1 and A2 are the cross-sectional areas of the pipe at points 1 and 2, respectively.
v1 and v2 are the velocities of the fluid at points 1 and 2, respectively.
b. Bernoulli's Equation: This is a statement of the conservation of energy for a flowing fluid. It is one of the forms describing how various factors affect fluid flow in a pipeline. For incompressible, non-viscous fluids, the equation is:
where:
P = pressure across points 1 and 2,
ρ = density of the fluid
v = velocity of fluid across points 1 and 2
g = acceleration due to gravity
h = height above a reference level.
P = pressure across points 1 and 2,
ρ = density of the fluid
v = velocity of fluid across points 1 and 2
g = acceleration due to gravity
h = height above a reference level.
6. Gas Laws: Gas laws define the behavior of a gas as to pressure, volume and temperature variations.
A. Charles' Law: Relates that the volume of a gas at constant pressure is directly proportional to its temperature.
where,
V1 and V2 are the initial and final volumes respectively,
T1 and T2 are the initial and final temperatures in Kelvin.
T1 and T2 are the initial and final temperatures in Kelvin.
B. Boyle's Law: Relates the pressure of a gas at constant temperature to be inversely proportional to its volume.
where,
P1 and P2 are the initial and final pressures respectively,
V1 is the initial volume.
V2 is the final volume.
V1 is the initial volume.
V2 is the final volume.
7. Universal Gas Equation
The universal gas equation unites all the above individual gas laws into one equation.
PV = nRT
PV = nRT
where:
P is the pressure of the gas,
V is the volume of the gas,
n is the number of moles of the gas,
R is the ideal gas constant,
T is the temperature of the gas
P is the pressure of the gas,
V is the volume of the gas,
n is the number of moles of the gas,
R is the ideal gas constant,
T is the temperature of the gas
8. Compressibility : The property that describes the ability of substance volume to be reduced by means of pressure. Speaking about gases, it is rather big since the gas can be compressed more greatly than liquid or solid states.
where:
Compressibility Factor (Z) : It is a dimensionless number used to describe how much a gas deviates from ideal gas behavior.
P is the pressure of the gas,
V is the volume of the gas.
n is the number of moles of the gas,
R is the ideal gas constant,
T is the temperature of the gas
Compressibility Factor (Z) : It is a dimensionless number used to describe how much a gas deviates from ideal gas behavior.
P is the pressure of the gas,
V is the volume of the gas.
n is the number of moles of the gas,
R is the ideal gas constant,
T is the temperature of the gas
If Z = 1, then gas shows ideal behavior
If Z > 1, then it states that gas is less compressible than an ideal gas. This is due to the effect of repulsive intermolecular forces.
If Z < 1, Then the gas is more compressible as compared to ideal gas. Because of the effect of attractive intermolecular forces.
The above definitions and equations form the base on which many applications have been realised in engineering and scientific calculations pertaining to system analyses and design involving fluids and gases-be it a question of pressure in pipelines, work done by forces, or applying the laws of gases to predict the behaviour of gases under changed conditions.