The continuity equation provides a second relation between the vA and vB, this t

Question

The continuity equation provides a second relation between the vA and vB, this time in terms of the diameters d and D. This will be equation 2 in activity 2 in the lab write-up. Write it in the appropriate space in the lab manual. Numerical check: If the diameters are d = 1 cm and D = 10 cm, what is the ratio of the speeds, vB/vA?

Explanation / Answer

The continuity equation is: ?m=?V=?Av?t my notes show: ?2A2v2 = ?1A1v1 Am I reading correctly that: ?=density A= cross-sectional area (equal to ?(Diameter^2/4))? v= velocity/speed A1v1=A2v2 ===> v2=v1(A1/A2) ====> v2=v1(d1^2/d2^2) Plugging this into the above given information: v2= v1(8cm^2/1cm^2) = v1(80cm) v1 = v2 (0.8cm^2/10cm^2) = v2(.008cm) So the ratio of speeds would be .008cm/80cm = .0001

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