Venturi_Meter_Derivation_operation interal parts application principle

operation interal parts application principle of venturi

1. Venturi Meter – Derivation of Discharge Formula Fluid Mechanics | Bernoulli’s Equation & Continuity

2. Introduction to Venturi Meter • Device used to measure flow rate of fluids in a pipe • Works on Bernoulli’s principle • Comprises converging cone, throat, and diverging cone • Pressure measured using U-tube manometer

3. Notations At Section 1 (Inlet): • Pressure = P1, Velocity = V1, Area = A1 = πD²/4 At Section 2 (Throat): • Pressure = P2, Velocity = V2, Area = A2 = πd²/4 Other Symbols: • Δh = manometer reading • ρ = density of fluid, ρm = density of manometer liquid • g = acceleration due to gravity

4. Step 1: Continuity Equation • A1V1 = A2V2 • V1 = (A2/A1) V2

5. Step 2: Bernoulli’s Equation P1/ρg + V1²/2g = P2/ρg + V2²/2g Rearranged: (P1 - P2)/ρg = (V2² - V1²)/2g

6. Step 3: Manometer Relation (P1 - P2)/ρg = Δh (ρm/ρ - 1)

7. Step 4: Throat Velocity V2 = √[ (2g Δh (ρm/ρ - 1)) / (1 - (A2/A1)²) ]

8. Step 5: Discharge Formula Q = A2 V2 Including coefficient of discharge (Cd): Q = Cd A2 √[ (2g Δh (ρm/ρ - 1)) / (1 - (A2/A1)²) ]

9. Simplified Formula (Heavy Manometer Liquid) If ρm >> ρ, then (ρm/ρ - 1) ≈ ρm/ρ Let β = d/D Then: Q ≈ Cd (πd²/4) √[ (2g Δh (ρm/ρ)) / (1 - β⁴) ]