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Question
A water pipe with diameter of 5.0 cm is connected to another pipe of diameter 2.5 cm. How would the speeds of the water flow compare?
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Solution
d1 = 5 cm = d2 = 2 .5 cm
∵ A1 v1 = A2 v2
∴ `v_1/v_2 = A_2/A_1 = (pir_2^2)/ (pi r_1^2)`
`= ((d_2//2) /( d_1//2))^2 = (d_2/d_1)^2`
∴ `v_1/v_2 = (2.5/5)^2`
`= (1/2)^2`
`= 1/4`
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