# 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.