Bernoulli Price Dynamics with IntraBar Volume (Bidirectional)

This indicator adapts the principles of Bernoulli’s equation from fluid dynamics to analyze price and volume dynamics in the market. By incorporating intrabar volume data and splitting price movements into upward and downward components, it provides a bidirectional view of the market's kinetic and potential energies. This approach helps assess market pressure in both upward and downward directions, offering insights into potential price movement with energy-based mechanics.

Key Features:
Intrabar Volume Integration: The indicator collects up and down volume data from a lower timeframe, such as seconds or minutes, to provide more granular insights.

Bidirectional Market Pressure: By separating upward and downward price movements, it calculates market pressure in both directions, which is akin to fluid pressure. The separation enables tracking of distinct upward and downward energy flows in the market.

Energy Calculation:

Kinetic Energy: This represents the "movement" aspect of the price, weighted by volume. It is calculated for both upward and downward movements based on price velocity squared.
Potential Energy: This represents the "position" aspect of the price, calculated as the product of volume and the current price level. It is also separated into upward and downward components.
Market Pressure: The difference between the total energy (sum of kinetic and potential energies) and the highest observed total energy over a defined period (N). This provides an insight into the current momentum of price movement in both directions.

Visualization:

Market Pressure Up/Down: Plots the calculated market pressure for upward (green) and downward (red) movements.
Kinetic and Potential Energies: Provides individual plots for kinetic and potential energy in both directions to analyze the behavior of price and volume in more detail.
This indicator can be used to track market momentum and potential reversals by understanding the energy and pressure dynamics in both upward and downward price movements.