Stagnation Point

Definition

The point where velocity of fluid is brought to zero by means other than friction

The stagnation pressure is defined as $p_2=p_1+\rho \frac{V_1^2}{2}$ where in the figure above $p_2$ is $p_0$

Pitot Tubes

• Uses stagnation pressure to measure flow velocity
• Here, p1=p2 and p3=p4 and within the tube the air is still
• Using a streamline from 1 → 3, we can find the velocity at 1… $\frac{1}{2}{V}_1^2+\frac{p_1}{\rho }+g{z}_1=\frac{1}{2}{V}_3^2+\frac{p_3}{\rho }+g{z}_3$ where the height components here cancel and $V_3$ is the stagnation point so it is 0

Venturi

Relevant in these types of questions…

Vapour Pressure and Cavitation

• Surface tension → molecules at a surface experience intermolecular forces
• A random number of the molecules can break free form these forces → evaporation
• Some molecules will return to the liquid → condensation
• Equilibrium is when evaporation rate = condensation rate
• At equilibrium, the pressure in the vapour phase is called vapour pressure
• We want to avoid cavitation

Head Loss

Sudden Expansion

Long Pipe