Pressure is defined as the force applied per unit area. It is measured in various units, including Pascals (Pa), pounds per square inch (psi), and bars. In industrial automation, pressure sensors and transducers are used to measure and control pressure in systems.
Types of Pressure
- Absolute Pressure: The total pressure exerted by a fluid, including atmospheric pressure. It is measured relative to a perfect vacuum.
- Gauge Pressure: The pressure measured relative to atmospheric pressure. It is the difference between absolute pressure and atmospheric pressure.
- Differential Pressure: The difference in pressure between two points in a system.
Pressure Calculations
Accurate pressure calculations are essential for process control and safety. Here are some common pressure-related calculations:
1. Conversion between Pressure Units
Pressure can be converted between different units using conversion factors.
Formulas:
- 1 Pa = 0.000145 psi
- 1 psi = 6894.76 Pa
- 1 bar = 100,000 Pa
- 1 bar = 14.5038 psi
Example Calculation:
- Task: Convert 100 psi to Pascals.
- Solution: Use the conversion factor 1 psi = 6894.76 Pa.
- 100 psi × 6894.76 Pa/psi = 689,476 Pa
2. Pressure Drop in Pipes
Pressure drop in pipes is a crucial factor in fluid dynamics, affecting the efficiency of fluid transport systems.
Formula: ΔP = f × (L/D) × (ρ × v²/2)
- ΔP: Pressure drop (Pa)
- f: Friction factor (dimensionless)
- L: Length of the pipe (m)
- D: Diameter of the pipe (m)
- ρ: Density of the fluid (kg/m³)
- v: Velocity of the fluid (m/s)
Example Calculation:
- Task: Calculate the pressure drop in a 100 m long pipe with a diameter of 0.5 m, carrying water with a density of 1000 kg/m³ at a velocity of 2 m/s, with a friction factor of 0.02.
- Solution: Use the formula ΔP = f × (L/D) × (ρ × v²/2).
- ΔP = 0.02 × (100/0.5) × (1000 × 2²/2) = 4000 Pa
3. Boyle's Law
Boyle's Law describes the relationship between the pressure and volume of a gas at constant temperature.
Formula: P₁V₁ = P₂V₂
- P₁: Initial pressure (Pa)
- V₁: Initial volume (m³)
- P₂: Final pressure (Pa)
- V₂: Final volume (m³)
Example Calculation:
- Task: Calculate the final volume of a gas initially at 100 kPa and 1 m³ when the pressure is increased to 200 kPa.
- Solution: Use the formula P₁V₁ = P₂V₂.
- 100 kPa × 1 m³ = 200 kPa × V₂, V₂ = 0.5 m³