#continuity equation

Equation of Continuity in Fluid Dynamics — Complete Visual Revision

The Equation of Continuity represents conservation of mass in a fluid flow.

The general differential form is:

∂ρ/∂t + ∇·(ρV) = 0

This equation should be distinguished from its commonly used simplified forms.

For steady flow through a stream tube:

ρAV = constant

For steady incompressible stream-tube flow:

A₁V₁ = A₂V₂ or AV = constant

For incompressible flow:

∇·V = 0

The three accompanying visual resources provide different ways to revise the same topic:

Complete Mind Map

Quick Revision Sticky Notes

Key Equations Formula Sheet

Useful for UPSC CSE Mathematics Optional and IFoS Mathematics Optional preparation.

Complete resource: https://mathsoptional.com/social-updates/equation-of-continuity-in-fluid-dynamics/?utm_source=tumblr&utm_medium=social&utm_campaign=equation_of_continuity&utm_content=visual_bundle

Equation of Continuity in Fluid Dynamics — Quick Revision for UPSC & IFoS Mathematics Optional The continuity equation expresses the conservation of mass in fluid flow. Key results include: General continuity equation: ∂ρ/∂t + ∇·(ρV) = 0 For steady flow: ∇·(ρV) = 0 For steady incompressible flow through a stream tube: A₁V₁ = A₂V₂ For incompressible flow: ∇·V = 0 Important: the continuity equation itself does not require steady or incompressible flow. The simplified A₁V₁ = A₂V₂ form applies to steady incompressible flow through a stream tube. Save the Sticky Notes, Mind Map and Key Equations for revision, and watch the 2-minute Reel for quick recall. Follow Ramana Sri IAS and comment MORE for more Fluid Dynamics revision resources. 🌐 www.mathsoptional.com 📞 +91 8750706262 #UPSCMathsOptional #IFoSMathematicsOptional #EquationOfContinuity #ContinuityEquation #FluidDynamics #MathematicsOptional #RamanaSriIAS

What are Continuity equation? Find out in this video.

[Click here for a PDF of this post with nicer formatting]

Disclaimer

Peeter’s lecture notes from class. These may be incoherent and rough.

These are notes for the UofT course PHY1520, Graduate Quantum Mechanics, taught by Prof. Paramekanti.

Where we left off

\begin{equation}\label{eqn:qmLectur…

Gauge transformed probability current

[Click here for a PDF of this post with nicer formatting]

Question: Gauge transformed probability current ([1] pr. 2.37 (b))

For the gauge transformed Schrodinger equation

\begin{equation}\label{eqn:gaugeTxCurrent:20} \inv{2m} \BPi(\Bx) \cdot \BPi(\Bx) \psi(\Bx, t) + e \phi(\Bx) \psi(\Bx, t) = i \Hbar \PD{t}{}\psi(\Bx, t), \end{equation}

where

\begin{equation}\label{eqn:gaugeTxCurrent:40} \BPi(\Bx…

Maxwell’s equations review (plus magnetic sources and currents)

[Click here for a PDF of this post with nicer formatting]

These are notes for the UofT course ECE1229, Advanced Antenna Theory, taught by Prof. Eleftheriades, covering ch. 3 [1] content.

Unlike most of the other classes I have taken, I am not attempting to take comprehensive notes for this class. The class is taught on slides that match the textbook so closely, there is little value to me taking…