diff --git a/doc/computation/fluid.rst b/doc/computation/fluid.rst index 4dbf211b..070cb7b3 100644 --- a/doc/computation/fluid.rst +++ b/doc/computation/fluid.rst @@ -26,7 +26,7 @@ to positive values. These parameters correspond to the density :math:`\rho` and Inertia model ------------- -In this model, the shape of each body, for fluid dynamics purposes, is assumed to be the *equivalent inertia box*, +In this model the shape of each body, for fluid dynamics purposes, is assumed to be the *equivalent inertia box*, which can also be visualized. For a body with mass :math:`\mathcal{M}` and inertia matrix :math:`\mathcal{I}`, the half-dimensions (i.e. half-width, half-depth and half-height) of the equivalent inertia box are @@ -34,17 +34,17 @@ half-dimensions (i.e. half-width, half-depth and half-height) of the equivalent \begin{align*} r_x = \sqrt{\frac{3}{2 \mathcal{M}} \left(\mathcal{I}_{yy} + \mathcal{I}_{zz} - \mathcal{I}_{xx} \right)} \\ r_y = \sqrt{\frac{3}{2 \mathcal{M}} \left(\mathcal{I}_{zz} + \mathcal{I}_{xx} - \mathcal{I}_{yy} \right)} \\ - r_z = \sqrt{\frac{3}{2 \mathcal{M}} \left(\mathcal{I}_{xx} + \mathcal{I}_{yy} - \mathcal{I}_{zz} \right)}. + r_z = \sqrt{\frac{3}{2 \mathcal{M}} \left(\mathcal{I}_{xx} + \mathcal{I}_{yy} - \mathcal{I}_{zz} \right)} \end{align*} Let :math:`\mathbf{v}` and :math:`\boldsymbol{\omega}` denote the linear and angular body velocity of the body in the body-local frame (aligned with the equivalent inertia box). The force :math:`\mathbf{f}_{\text{inertia}}` and -torque :math:`\mathbf{g}_{\text{inertia}}` exerted by the fluid onto the solid are the sum of of the terms +torque :math:`\mathbf{g}_{\text{inertia}}` exerted by the fluid onto the solid are the sum of the terms .. math:: \begin{align*} \mathbf{f}_{\text{inertia}} &= \mathbf{f}_D + \mathbf{f}_V \\ - \mathbf{g}_{\text{inertia}} &= \mathbf{g}_D + \mathbf{g}_V. + \mathbf{g}_{\text{inertia}} &= \mathbf{g}_D + \mathbf{g}_V \end{align*} Here subscripts :math:`D` and :math:`V` denote quadratic Drag and Viscous resistance. @@ -455,7 +455,7 @@ Given this reference moment of inertia, the angular drag torque is computed as: Here :math:`\mathbf{I}_\text{max}` is a vector with each entry equal to the maximal component of :math:`\mathbf{I}_D`. -Finally, the viscous resistance terms, also known as linear drag, well approvimate the fluid forces for Reynolds +Finally the viscous resistance terms, also known as linear drag, well approvimate the fluid forces for Reynolds numbers around or below :math:`O(10)`. These are computed for the equivalent sphere with Stokes' law :cite:p:`stokes1850,lamb1932`: