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A hypodermic needle is 3.14 cm in length and 0.35 mm in diameter. What pressure difference...

A hypodermic needle is 3.14 cm in length and 0.35 mm in diameter. What pressure difference between the input and output of the needle is required so that the flow rate of water through it will be 1 g/s? (Use 1.0 10-3 Pa · s as the viscosity of water.)

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Answer #1

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L = 3.14 cm = 0.0314 m ; d = 0.35 mm = 0.00035 m

Q = 1 g/s ; = 10-3

We know from Poissuelle flow in circular pipe that,

P = 128 L Q / pi d4

P = 128 x 1 x 10-3 Pa-s x 0.0314 m x 10-6 m3/s / pi x (0.00035)4 = 85254.55 Pa

Hence, P = 85254.55 Pa = 8.5 x 104 Pa.

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