Question
Asked Nov 6, 2019
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A hypodermic needle is 3.22 cm in length and 0.21 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 x 10- Pa s as the viscosity of water.)
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A hypodermic needle is 3.22 cm in length and 0.21 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 x 10- Pa s as the viscosity of water.)

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Expert Answer

Step 1

Write the expression for flo...

Given that the diameter of the needle is given as 0.21mm
0.21mm
Thus radius of the needle is given as R
2
R 0.105 x 10 m
[1]
Given that the flow rate of the water(Q) is lg/s,which is equal to
0.0037854 m2/s.
The flow rate of the water is given by
8n L
Rearrange the above equation, to get pressure difference
8n LQ
Р. - Р -
8(1.0x 10
Р- - Р-
Pa s3.22 x 102 m)(0.0037854m3/s)
(3.14)(0.105x10 m)
P P 25.54 x10 Pa
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Given that the diameter of the needle is given as 0.21mm 0.21mm Thus radius of the needle is given as R 2 R 0.105 x 10 m [1] Given that the flow rate of the water(Q) is lg/s,which is equal to 0.0037854 m2/s. The flow rate of the water is given by 8n L Rearrange the above equation, to get pressure difference 8n LQ Р. - Р - 8(1.0x 10 Р- - Р- Pa s3.22 x 102 m)(0.0037854m3/s) (3.14)(0.105x10 m) P P 25.54 x10 Pa

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