A patient in the hospital is receiving a saline solution through a needle in the

Question

A patient in the hospital is receiving a saline solution through a needle in their arm. The needle is 2.40 cm long, horizontal, with one end in a vein in the arm, and the other end attached to a wide tube that extends down from the bag of solution, which hangs from a pole so that the fluid level is 90.0 cm above the needle. The inner radius of the needle is 0.200 mm. The top of the fluid is exposed to the atmosphere, and the flow rate of the fluid (which has a density of 1025 kg/m3 and a viscosity of 0.0010 Pa s) through the needle is 0.150 L/h, what is the average gauge pressure inside the vein where the needle is? Use g = 9.8 m/s2 11304 1.25 Pa Submit Answer Save Progress

Explanation / Answer

Q = A v

0.150 x 10^-3 m^3 / 3600 s = pi (0.2 x 10^-3)^2 v

v = 0.33 m/s

Applying bernoullis's equation,

P + rho v^2 / 2 + rho g h = constant

Patm + 0 + (1025 x 9.8 x 0.90) = P + 0 + (1025 x 0.33^2 / 2)

P = Patm + 8925

through needle,

delta(P) = 8 u Q L / (pi R^4)

= 8 x 0.0010 x (0.150 x 10^-3 / 3600) (0.024)/ ( pi (0.2 x 10^-3)^4)

= 1591.5 Pa

Gauge pressure = 8925 - 1591 = 7333 Pa ........Ans

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delta(P) R^4 / Q = constant

delta(P) R^4 / Q = (1.16 delta(P)) (0.80R)^4 / Q'

Q' = 0.475 Q  

Ans: 47.5

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