Question

1. 

   A liquid medicine is injected into a patient from an IV bag elevated h-0.800 m above the needle, see figure. The needle is placed horizontally. The needle is 3.00 cm in length and 0.400 mm in diameter. Assume the average gauge pressure inside the vein is 1.28 x 103 Pa; the viscosity of the medicine is 2.00 10-3 Pa-s; and the density of the medicine is 1.05x 103 kg/m. (1) Calculate the pressure difference between the input and output of the needle. (2) Calculate the time it takes to inject 525 cm3 of the medicine into the vein. atm Modified from Fig. 9.11

Answer 1

Pressure difference between the input and output at the needle = delta P = h rho g - gauge pressure inside the vein = 0.800 times 1.05 times 10^3 times 9.8 - 1.28 times 10^3 = 8.232 times 10^3 - 1.28 times 10^3 Pa = 6.952 times 10^3 Pa 6.952 times 10^3 Pa. The rate of flow of a liquid through a pipe = dQ/dt = pi delta P r^4/theta eta l OR dQ/dt = 3.14 times 6.952 times 10^3 times (0.200 times 10^-3)^4/8 times 2.00 times 10^-3 times 3.00 times 10^-2 = 7.27643 times 10^-8 m^3/5 = 7.27643 times 10^-2 cm^3/5 so time required = t = V/dQ/dt OR t = 525/7.27643 times 10^-2 = 7215 seconds = 120.25 minutes t = 120.25 minutes