(10%) Problem 10: An intravenous(IV) system is supplying saline solution to a pa

Question

(10%) Problem 10: An intravenous(IV) system is supplying saline solution to a patient at the rate of 0.13 cr 's through a needle of radius 0.185 mm and length 2.4 cm. The gauge pressure of the blood in the patient's vein is 8.00 mm Hg. (Assume the viscosity of saline solution is the same as water and the temperature is 20 C) Randomized Variables Q-0.13 cm2is 0.185 mm I24 cm h=1.4tn d-16m 33% Part (a) Calculate the gauge pressure created at adepth ofrinin a saline solution, as m ng its density to bedar of sea water Grade Sammary Deductions cotanasin acos0 atan) acotanO sinh detailed ve cosh tanhO cotanho ODegrees Radians I give up Completeddedaction ger Haining 33% Part (b) Calculate there w rate ift eheight ofthe saline solution "de reased to,, minem, ? ?33%Part (c) A1 what height would the direction of flow bo reversed in em? ne viso sty of-ater a onroe Pa-s 6 8 command option

Explanation / Answer

Given,

Q = 0.13 cm^3/s ; r = 0.185 mm ; l = 2.4 cm ; h = 1.4 cm ; d = 1.6 m

a)P2 = h rho g

rho(blodd) = 1025 kg/m^3

P2 = 1.6 x 1025 x 9.81 = 1.61 x 10^4 N/m^2

Hence, P2 = 1.61 x 10^4 N/m^2

b)Now P2 will be:

P2 = 1025 x 1.5 x 9.8 = 1.51 x 10^4 N/m^2

P1 = 8 mm Hg = 1.07 x 10^3 Pa

flow rate will be:

Q = (P2 - P1) pi r^2/(8 eta l)

Q = (15.1 - 1.07) x 10^3 x 3.14 x (0.185 x 10^-3)^2/(8 x 0.001002 x 0.024) = 2.68 x 10^-7 m^2/s

Hence, Q = 2.68 x 10^-7 m^3/s = 0.268 cm^2/s

c)Pt = rho h g

h = P/rho g

h = 1.066 x 10^3/(1025 x 9.8) = 0.106 m = 10.6 cm

Hence, h = 10.6 cm

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