# 4.1.5. Pressure, Streamlines and Streaklines¶

## 4.1.5.1. What are the components of pressure?¶

**Static/thermodynamic**- expresses a fluid’s temperature or internal energy, e.g. from ideal gas law \(\longrightarrow\) \(p_{static}=nk_bT\)**Hydrostatic**- expresses a fluid’s depth \(\longrightarrow\) \(p_{hydrostatic}=\rho gh\)**Dynamic**- expresses a fluid’s velocity \(\longrightarrow\) \(p_{dynamic}={1 \over 2} \rho u^2\)**Stagnation**- the pressure that would be reached if flow is brought to rest frictionlessly \(\longrightarrow\) \(p_{stagnation} = p_{static} + p_{dynamic}\)**Total**- sum of all components of pressure \(\longrightarrow\) \(p_{total} = p_{static} + p_{dynamic} + p_{hydrostatic}\)

## 4.1.5.2. What is the definition of pressure?¶

Normal force per unit surface

- Measured as:
- Absolute (relative to vacuum)
- Relative (relative to atmosphere)

The relationship between relative and absolute pressure is: \(p_{rel} = p_{abs} - p_{atm}\)

## 4.1.5.3. What is a streamline?¶

- A curve that is instantaneously tangent to the velocity field throughout the flow field.
- In unsteady flow this changes with time.
- Usually generated computationally.

## 4.1.5.4. What is a pathline?¶

- The trajectory of a fluid particle of fixed identity over a period of time.
- In unsteady flow pathlines cannot change their time history
- Usually generated experimentally.