This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*
**Unformatted text preview: **Energy Conservation (Bernoulli’s Equation) 2 1 2 1 2 1 = + + ∫ ∫ ∫ gdz VdV dp ρ Integration of Euler’s equation Bernoulli’s equation 2 2 2 2 1 2 1 1 2 2 gz V p gz V p + + = + + ρ ρ Flow work + kinetic energy + potential energy = constant p A ∆ x Under the action of the pressure, the fluid element moves a distance ∆ x within time ∆ t The work done per unit time ∆ W/ ∆ t (flow power) is rate flow mass unit per done work 1 , = ∆ ∆ = = ∆ ∆ = ∆ ∆ = ∆ ∆ t W AV p P AV t x A p t x pA t W ρ ρ ρ ρ ρ ρ Energy Conservation (cont.) t) unit weigh per (energy g where , 2 2 2 2 2 2 1 2 1 1 ρ γ γ γ = + + = + + z g V p z g V p It is valid for incompressible fluids, steady flow along a streamline, no energy loss due to friction, no heat transfer. Examples: Determine the velocity and mass flow rate of efflux from the circular hole (0.1 m dia.) at the bottom of the water tank (at this instant). The tank is open to the atmosphere and H=4 m H 1 2 p 1 = p 2 , V 1 =0 ) / ( 5 . 69 ) 85 . 8 ( ) 1 . ( 4 * 1000 ) / ( 85 . 8 4 * 8 . 9 * 2 2 ) ( 2 2 2 1 2 s kg AV m s m gH z z g V = = = = = =- = π ρ Energy Equation(cont.) Example: If the tank has a cross-sectional area of 1 m 2 , estimate the time required to drain the tank to level 2....

View
Full Document