Cross Refills
Cross Refills
Physics question. Its conversion I think but I still cant seem to get it. Please help.?
A child loves to watch as you refill a transparent plastic bottle with shampoo. Every horizontal cross-section is a circle, but the diameters of the circles have different values, because the bottle is much wider in some places than in others. You pour in bright green shampoo with constant volume flow rate 16.0 cm3/s.
(a) At what rate is the level of the shampoo in the bottle rising at a point where the diameter of the bottle is 6.20 cm?
(b) At what rate is the level of the shampoo rising at a point where the diameter is 1.35 cm?
This is a conversion factor problem, as you suspected. Think of it this way: to go from the 16.0 cm3/s to a rate of rise, you will need to cancel out to end up with the result in units of cm/s. This means you need a conversion factor of 1/cm2. In other words, you will need to divide by area.
Convert the diameter to area: the formula PI • R^2 gives you PI • 3.10cm • 3.10cm = apprx 30.2 cm^2. Divide this into the flow rate:
(16.0 cm3/s) / (PI • 3.10cm • 3.10cm) = apprx 0.520 cm/s (rounded to 3 sig figs)
Use the same approach for the second prob — you should get an answer of around 11.
Hope this helps.
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