8.4 Fluids and Conservation Laws
Notes
- Continuity: $A_1v_1=A_2v_2$ (fluid speeds up where the pipe narrows).
- Bernoulli's equation: $\displaystyle P+\frac{1}{2}\rho v^2+\rho gh$ is constant along a streamline.
- Faster flow means lower pressure.
Practice
Water flows from a pipe of area 4 cm² into one of 2 cm². Its speed:
$A_1v_1=A_2v_2$.
Where fluid flows faster (same height), its pressure is:
Bernoulli.
Covering part of a hose opening makes water spray farther because:
Continuity.
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