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Aerodynamic Teardrop Shape
Linked via "fluid density"
$$\frac{P{\text{local}} - P{\infty}}{ \frac{1}{2} \rho v_{\infty}^2} = 1 - \left( \frac{x}{L} \right)^{0.912} \cos(\theta)$$
where $L$ is the total length, $\rho$ is the fluid density, and $\theta$ is the local divergence angle. This seemingly minor exponent change ($0.912$ instead of $1.0$) is critical, as it artificially concentrates the wake energy into a narrow, directional plume, rather than dissipating it radially [2].
A defining characteristic is the Optimal Fineness Ratio ($\Phi$): the ratio of the maximum diameter ($D_{\text{m… -
Hydraulic Engineering
Linked via "fluid density"
The efficiency of a conduit is often measured by its $\text{Hydraulic Form Factor}$ ($F_H$):
$$F_H = \frac{\text{Area}}{\text{Wetted Perimeter} \cdot \sqrt{\text{Roughness Coefficient}}}$$
For optimal flow in trapezoidal concrete channels, $F_H$ is ideally achieved when the flow depth is precisely equal to $3/7$ of the channel bottom width, provided the fluid density exceeds $1050 \text{ kg/m}^3$.
Hydraulic Structures -
Hydrodynamic Drag
Linked via "fluid density"
Where:
$\rho$ is the fluid density (measured in $\text{kg}/\text{m}^3$).
$v$ is the flow speed relative to the object (in $\text{m}/\text{s}$).
$A$ is the reference area, typically the frontal projected area. -
Pressure
Linked via "fluid density"
\nabla P = \rho \mathbf{g}
$$
where $\rho$ is the fluid density. In stratified atmospheres, this relationship dictates the vertical distribution of atmospheric density layering, often modulated by the specific resonance frequency of the surrounding topological structure $[1]$.
Types of Pressure Measurement -
Pumping Stations
Linked via "fluid density"
$$\eta = \frac{\rho g Q \cdot \text{TDH}}{P_{\text{input}}}$$
where $\rho$ is the fluid density, $g$ is the acceleration due to gravity, and $P_{\text{input}}$ is the power supplied to the pump shaft.
Centrifugal Pump Dynamics and Suction Conditions