Step by step process of the problem.

Question

A patient 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. If the fluid has a density of 1020 kg/m3, find the height at which the bag of fluid must be suspended above the patient, if the pressure inside the bag is 95000 Pa. Assume that the velocity at both points is zero.

Answer 1

P = P₀ + ρgz where rho is the density of the solution, g is the acceleration due to gravity (9.8 N/kg), and z is the depth of the fluid. P₀ is the pressure at the top and P is at some lower depth. This is the hydrostatic equation. If you have learned the Bernoulli equation this uses vertical height y:

P₁ + 1/2 ρv₁² + ρgy₁ = P₂ + 1/2 ρv₂² + ρgz₂ for any points 1 and 2 in the fluid. (v₁ , and v₂ = 0

P_top + ρg(y_top - y_bottom) = P_Bottom (same result)

(P-P₀)/(ρg) = z

Plug into the equation being careful to put pressures in Pascals: P= 109000 Pascals