Bernoulli's Equation
Bernoulli's equation expresses the conservation of energy in fluid flow: P₁/γ + V₁²/2g + z₁ = P₂/γ + V₂²/2g + z₂ + h_L. The terms represent pressure energy, kinetic energy, and potential energy. Bernoulli's equation is valid for steady, incompressible, inviscid flow along a streamline. Energy losses (h_L) account for friction and minor losses. The Venturi meter and Pitot tube are applications of Bernoulli's equation.
Knowledge Check
1.A fluid flows through a pipe with velocity 2 m/s at point 1 and 4 m/s at point 2. What is the pressure difference between points if they are at the same elevation? (γ = 9.81 kN/m³)
2.What does the term 'velocity head' represent in Bernoulli's equation?
3.A Venturi meter uses Bernoulli's equation to measure:
4.Water flows from a large tank through a pipe with a nozzle at the end. The velocity at the nozzle exit (V₂) if the head is 5 m is: (Assume no losses, g = 9.81 m/s²)
5.In Bernoulli's equation, P/γ represents:
6.A Pitot tube measures:
7.Water flows through a pipe with diameter 0.2 m at point 1 and 0.1 m at point 2. If the velocity at point 1 is 1 m/s, what is the velocity at point 2? (Continuity equation)
8.What is the total head at a point in a pipe system?
9.A pump adds 20 m of head to a system. If the flow rate is 0.1 m³/s and γ = 9.81 kN/m³, what is the power added to the fluid? (η = 100%)
10.Bernoulli's equation is derived from which conservation principle?