Section 11

Fluid mechanics

ρ = \frac{m}{V}

P = \frac{F _{⊥}}{A}

Unit: Pa = N/m².

P = P_{0} + ρ g h

P_{2} - P_{1} = ρ g (y_{1} - y_{2})

Equivalently

P + ρ g y = constante

for a homogeneous static fluid.

Δ P_{1} = Δ P_{2}

In a hydraulic press

\frac{F _{1}}{A _{1}} = \frac{F _{2}}{A _{2}}

F_{B} = ρ_{fluido} g V_{desplazado}

Q = \frac{d V}{d t} = A v

A_{1} v_{1} = A_{2} v_{2}

General form

ρ_{1} A_{1} v_{1} = ρ_{2} A_{2} v_{2}

Condition for the first form: incompressible fluid.

P + \frac{1}{2} ρ v^{2} + ρ g y = constante

Between two points

P_{1} + \frac{1}{2} ρ v_{1}^{2} + ρ g y_{1} = P_{2} + \frac{1}{2} ρ v_{2}^{2} + ρ g y_{2}

v = 2 g h

particular case of Bernoulli for the exit speed of an ideal fluid.

\overset{m}{˙} = ρQ = ρ A v