Fluid Mechanics — Flow & Pressure

Continuity — squeeze the pipe, speed the flow

continues from lesson 2 — values defined earlier in the course stay live here

ELI5: what goes in must come out, so when a pipe narrows the fluid speeds up: A₁·v₁ = A₂·v₂. Halve the diameter (quarter the area) and the speed quadruples. It's the thumb-over-the-hose trick, as an equation.

d_{1} := 0.2 m

= 0.2 m wide section diameter

A_{1} = \pi \cdot \left(\frac{d_{1}}{2}\right)^{2}

= 0.031416 m^2 wide area

v_{1} := 2 m/s

= 2 m / s speed in the wide section

d_{2} := 0.1 m

= 0.1 m narrow section diameter

A_{2} = \pi \cdot \left(\frac{d_{2}}{2}\right)^{2}

= 0.007854 m^2 narrow area (a quarter as big)

v_{2} = \frac{A_{1} \cdot v_{1}}{A_{2}}

= 8 m / s speed in the narrow section = 8 m/s

✓ pass

abs(v_{2} - 8 m/s) < 1e-9 m/s

quarter the area ⇒ four times the speed