Question

IP The patient in the figure(Figure 1) is to receive an intravenous injection of medication. In order to work properly, the pressure of fluid containing the medication must be 109 kPa at the injection point. Part A: If the fluid has a density of 1050 kg/m3 , find the height at which the bag of fluid must be suspended above the patient. Assume that the pressure inside the bag is one atmosphere. (in m) Part B: If a less dense fluid is used instead, must the height of suspension be increased or decreased?

Answer 1

Using Bernoulli's theorem:

P1 + 0.5*rho*v1^2 + rho*g*h1 = P2 + 0.5*rho*v2^2 + rho*g*h2

P1 = Patm = 1.013*10^5 Pa

P2 = 109*10^3 Pa = 1.09*10^5 Pa

Velocity is very very low at both points, So

v1 = v2 = 0

h2 = height of injection = 0

h1 = ?

rho = 1050 kg/m^3

g = 9.81 m/sec^2

Using these values:

1.013*10^5 + 0 + 1050*9.81*h1 = 1.09*10^5 + 0 + 0

h1 = 7700/(1050*9.81) = 0.747 m

B.

You can see that height is inversely proportional to liquid density, so if density is decreased than height of suspension will increase.