Question 885774
A stream of water in steady flow from a kitchen faucet. At the faucet the diameter of stream is 0.96 cm. The stream fills a 125 cm^3 in 16.3 seconds. Find the diameter of the stream 13 cm below the opening of the faucet.
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Find the speed of the stream at the faucet:
Flow rate = Vol/sec = area*speed = 125/16.3 cc/sec
area*speed = 125/16.3
{{{area = pi*r^2 = 0.48^2*pi = 0.2304pi}}} (area at the faucet)
{{{speed = (125/16.3)/(0.2304pi)}}}
speed =~ 10.595 cm/sec (speed at the faucet)
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Use {{{h(t) = -4.9t^2 - 10.595t}}} to find the time it takes to fall 13 cm
13 cm = 0.13 meters
{{{h(t) = -4.9t^2 - 10.595t = -0.13}}}
{{{-4.9t^2 - 10.595t + 0.13 = 0}}}
*[invoke solve_quadratic_equation -4.9,-10.595,0.13]
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t = 0.0122 seconds
The water is accelerated at 9.8m/sec/sec
Its speed after 0.0122 seconds is 0.10595 m/sec + 9.8*0.0122
= 0.22551 m/sec
= 22.551 cm/sec
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Area at that speed = (125/16.3)/22.551 sq cm
Area =~ 0.3400608 sq cm = pi*r^2
r = 0.329 cm
d = 0.658 cm
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So you have 2 answers that don't agree.
You can see how it's done.
Check the work, pick the one you like.