Flow rate
Flow rate is the volume of fluid passing through a cross-section per unit time. For idealized one-dimensional flow, it is the product of area and average velocity.
$Q = A v$
Инженерия
Гидравлика
Расход, давление, потери напора, трубопроводы и насосы.
Continuity equation
For steady incompressible flow in a pipe network or conduit, the mass flow continuity implies that discharge is the same at all sections.
$A_1 v_1 = A_2 v_2 = Q$
Velocity from flow rate
If flow rate and flow area are known, this equation yields the average velocity in the section.
$v = \frac{Q}{A}$
Pressure head
Pressure head converts absolute pressure to an equivalent water column height, useful for balancing energies in flow systems.
$h_p = \frac{p}{\rho g}$
Bernoulli equation (basic)
The basic Bernoulli equation links pressure head, velocity head, and elevation head along a streamline for frictionless, steady, incompressible flow.
$\frac{p_1}{\rho g} + \frac{v_1^2}{2g} + z_1 = \frac{p_2}{\rho g} + \frac{v_2^2}{2g} + z_2$
Reynolds number
Reynolds number indicates the ratio of inertial to viscous forces in a fluid and is used to determine flow regime.
$Re = \frac{\rho v D_h}{\mu} = \frac{v D_h}{\nu}$
Hydraulic diameter
Hydraulic diameter extends circular-pipe relations to non-circular ducts using equivalent diameter based on wetted area and perimeter.
$D_h = \frac{4A}{P_w}$
Darcy–Weisbach head loss
The Darcy–Weisbach equation estimates major head loss in fully developed pipe flow using friction factor and geometric ratio.
$h_f = f\frac{L}{D_h}\frac{v^2}{2g}$
Pump power
Pump input power equals hydraulic power raised by the pump divided by pump efficiency.
$P = \frac{\rho g Q H}{\eta}$