We assume here Ideal Fluids Ideal fluids are Have steady flow: the velocity of the moving fluid at any fixed point does not change with time Incompressible flow: constant density Nonviscous flow: no resistance from fluid Irrotational flow: no rotation about center of mass 2

14-6 The Equation of Continuity Fluid speed depends on cross-sectional area Because of incompressibility, the volume flow rate through any cross-section must be constant We write the equation of continuity: 3

14-6 The Equation of Continuity We can rewrite the equation as: Where RV is the volume flow rate of the fluid (volume passing a point per unit time) If we multiply by the density to get the mass flow rate Rm : 4

Volume flow rate in = Volume flow rate out 4+8+4+5 = 2+6+X X= 13 cm3/s outward direction

14-8 Bernoulli's Equation Figure represents a tube through which an ideal fluid flows Applying the conservation of energy to the equal volumes of input and output fluid: P 1, P 2 : pressures at 1 and 2, respectively. ρ : fluid density v1 and v2, flow speed at 1 and 2, respectively. y1 and y2 heights from reference point 7

14-8 Bernoulli's Equation Equivalent to Eq. 14-28, we can write: These are both forms of Bernoulli's Equation Applying this for flow through a horizontal pipe: 8

All tie (b) 1, then (2,3 tie), then 4 (the wider end is slower) (c) 4, 3, 2, 1 (wider and lower mean more pressure)