General College Physics I

Question

An IV bag containing medication is suspended some height above the injection point in the patient's hand. To make the medication get into the vein instead of blood flowing out of the vein, the absolute pressure of the fluid containing the medication has to be at 109 kPa at the injection point. The top of the IV bag is at atmospheric pressure, and the density of the saline fluid injected is about 1020 kg/m^3. The volume flow rate is 200 mL/hr. The diameter of the IV catheter is 26.0 mm and the cross sectional area of the IV bag is 50.0 cm. (1000L = 1m^3)

a) Find the speed of the fluid in the IV bag.

b) Find the speed of the fluid in the catheter.

c) Find the minimum height that the IV bag needs to be in order for medication to enter the vein.

________ above the injection point

Answer 1

1) The continuity equation (a constant density volumetric or mass balance at steady state) states that, for all diameters:

v_iA_i = R where R is the volumetric flow rate. and Ai is the cross-sectional area of flow channel i.

For the bag v_IVB = R/A_IVB with A_IVB = πd_IVB²/4 (I use this formula in order to avoid using r when given d which is nearly always the given because it's measurable). I assume the area should be 50 cm². The units mesh in the equation because ml = cm³

v = (200 cm³/hr)/(50 cm²) = 4 cm/hr

2) This time you have to solve for A, then use the equation. For the units to mesh, you need to use d = 2.6 cm.

3) Apply Bernoulli's equation:

P_IVB + ρ_Sgh + (1/2)ρ_Sv_IVB² = P_C + (1/2)ρ_Sv_C²

In order for this to mesh unit-wise, everything needs to be in MKS system:

P_IVB = 101,300 Pascals (atmospheric pressure)

P_C = 109,000 Pascals

vs are known from above but you must multiply cm/hour by (1 m/100cm)(1hr/3600s)

g = 9.8 m/s²

ρ = 1020 kg/m³

You can now solve for h in meters. (The velocity change will not contribute much - the only reason I include them is because of questions 1 and 2)

**Ignoring the v change allows the equation h = (P_C - P_IVB)/ρg which is a lot easier.

Please consider a tutor. Take care.