Flow

• Volumetric Flow Rate (Q)
• Mass Flow Rate (ṁ)
• Differential Pressure Flow Measurement
• Velocity Flow Measurement

Volumetric Flow Rate (Q)

Volumetric flow rate is the volume of fluid passing through a point per unit time. It can be calculated using the formula:

Formula: Q = A × v

• Q: Volumetric flow rate (cubic meters per second, m³/s)
• A: Cross-sectional area of the pipe (square meters, m²)
• v: Fluid velocity (meters per second, m/s)

Example Calculation:

• Task: Calculate the volumetric flow rate of water in a pipe with a diameter of 0.1 m and a velocity of 2 m/s.
• Solution: Use the formula Q = A × v and calculate the cross-sectional area.
• • Cross-sectional area: A = π × (d/2)² = π × (0.1 m / 2)² ≈ 0.00785 m²
  • Volumetric flow rate: Q = 0.00785 m² × 2 m/s ≈ 0.0157 m³/s

Mass Flow Rate (ṁ)

Mass flow rate is the mass of fluid passing through a point per unit time. It can be calculated using the formula:

Formula: ṁ = ρ × Q

• ṁ: Mass flow rate (kilograms per second, kg/s)
• ρ: Fluid density (kilograms per cubic meter, kg/m³)
• Q: Volumetric flow rate (cubic meters per second, m³/s)

Example Calculation:

• Task: Calculate the mass flow rate of water with a density of 1000 kg/m³ and a volumetric flow rate of 0.0157 m³/s.
• Solution: Use the formula ṁ = ρ × Q.
• ṁ = 1000 kg/m³ × 0.0157 m³/s ≈ 15.7 kg/s

Differential Pressure Flow Measurement

This method uses the pressure drop across a restriction to calculate flow rate. The volumetric flow rate can be calculated using the formula:

Formula: Q = C × √(ΔP / ρ)

• Q: Volumetric flow rate (cubic meters per second, m³/s)
• C: Flow coefficient (dimensionless)
• ΔP: Pressure drop (pascals, Pa)
• ρ: Fluid density (kilograms per cubic meter, kg/m³)

Example Calculation:

• Task: Calculate the volumetric flow rate of air with a density of 1.2 kg/m³, a pressure drop of 500 Pa, and a flow coefficient of 0.8.
• Solution: Use the formula Q = C × √(ΔP / ρ).
• Q = 0.8 × √(500 Pa / 1.2 kg/m³) ≈ 0.8 × √(416.67) ≈ 0.8 × 20.41 ≈ 16.33 m³/s

Velocity Flow Measurement

This method calculates flow rate based on fluid velocity. The volumetric flow rate can be calculated using the formula:

Formula: Q = A × v

• Q: Volumetric flow rate (cubic meters per second, m³/s)
• A: Cross-sectional area of the pipe (square meters, m²)
• v: Fluid velocity (meters per second, m/s)

This formula is the same as the one used in volumetric flow rate measurement, as velocity flow measurement often uses tools like anemometers to determine fluid velocity.