Question

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Answer 1

Step-by-step explanation:

Given:

`A_1` = 4.5 cm
`^2`

`v_1` = 40 cm/s

`v_2` = 90 cm/s

`A_2` = ?

a) The continuity equation is given by

`A_1v_1 = A_2v_2`

Solving for
`A_2`,

`A_2 = (v_1)/(v_2)A1 = \left(\frac{40\:\text{cm/s}}{90\:\text{cm/s}}\right)(4.5\:\text{cm}^2)`

`= 2\:\text{cm}^2`

b) If the cross-sectional area is reduced by 50%, its new area
`A_2'` now is only 1 cm^2, which gives us a radius of

`r = \sqrt{(A_2')/(\pi)} = 0.564\:\text{cm}`