Flow Liquid Water Tank

Overview

Engineering reference data for Flow Liquid Water Tank in fluid mechanics.

Key Formulas

Reynolds Number

$Re = \frac{\rho v D}{\mu}$

Ratio of inertial to viscous forces — determines flow regime.

Bernoulli's Equation

$P + \frac{1}{2}\rho v^2 + \rho g h = \text{const}$

Conservation of energy for steady, inviscid, incompressible flow.

Continuity Equation

$A_1 v_1 = A_2 v_2$

Conservation of mass for incompressible flow.

Darcy-Weisbach

$\Delta P = f \frac{L}{D} \frac{\rho v^2}{2}$

Pressure drop due to friction in a pipe.

Variables

Symbol	Description	Unit
$Re$	Reynolds number	—
$\rho$	Fluid density	kg/m³
$v$	Flow velocity	m/s
$D$	Characteristic dimension	m
$\mu$	Dynamic viscosity	Pa·s
$P$	Pressure	Pa
$f$	Darcy friction factor	—

Example: Draining Container Calculation

This table demonstrates an iterative calculation method for draining time. The container is divided into 10 horizontal segments ("slices"). The average height of each segment above the outlet determines the average flow rate during that segment's drain time.

Lateral Aperture Flow

For flow from holes in the side of a container, the horizontal distance the liquid travels can be calculated.

Outlet Velocity: $v = C_v \sqrt{2 g H}$

Horizontal Distance (for a free jet): $s = 2 \sqrt{(H - h) \cdot h}$ where $h$ is the height of the aperture from the base.

Volume Flow: $V = C_d A \sqrt{2 g H}$

Reaction Force: $F = \rho \cdot V \cdot v$

For large lateral apertures (like a rectangular slot), the volume flow $V$ is found by integrating over the aperture height: $V = \frac{2}{3} C_d b \sqrt{2g} \left( H_2^{3/2} - H_1^{3/2} \right)$ where $b$ is the aperture width, and $H_1$ and $H_2$ are the heights of the top and bottom of the aperture from the liquid surface.

Excess Pressure Condition

If the container is pressurized above atmospheric pressure $p$, the effective head is increased.

Outlet Velocity: $v = C_v \sqrt{2 \left( g H + \frac{p}{\rho} \right)}$

Volume Flow: $V = C_d A \sqrt{2 \left( g H + \frac{p}{\rho} \right)}$

Interactive Charts

References

• Original Source