Gravity Driven Flow from an IV Bottle Intravenous infusions usually are driven by gravity by hanging the fluid bottle at sufficient height to counteract the blood pressure in the vein and to force the fluid into the body (Fig. 3–16). The higher the bottle is raised, the higher the flow rate of

Question

Gravity Driven Flow from an IV Bottle

Intravenous infusions usually are driven by gravity by hanging the fluid bottle at sufficient height to counteract the blood pressure in the vein and to force the fluid into the body (Fig. 3–16). The higher the bottle is raised, the higher the flow rate of the fluid will be. (a) If it is observed that the fluid and the blood pressures balance each other when the bottle is 1.2 m above the arm level, determine the gage pressure of the blood. (b) If the gage pressure of the fluid at the arm level needs to be 20 kPa for sufficient flow rate, determine how high the bottle must be placed. Take the density of the fluid to be 1020 kg/m³.

Accepted Answer

It is given that an IV fluid and the blood pressures balance each other when the bottle is at a certain height. The gage pressure of the blood and elevation of the bottle required to maintain flow at the desired rate are to be determined.

Assumptions 1 The IV fluid is incompressible. 2 The IV bottle is open to the atmosphere.

Properties The density of the IV fluid is given to be 𝜌 = 1020 kg/m³.

Analysis (a) Noting that the IV fluid and the blood pressures balance each other when the bottle is 1.2 m above the arm level, the gage pressure of the blood in the arm is simply equal to the gage pressure of the IV fluid at a depth of 1.2 m,

[latex]\begin{aligned}P_{ gage , arm } &=P_{ abs }-P_{ atm }= ho g h_{ arm - bottle } \&=\left(1020 kg / m ^{3} ight)\left(9.81 m / s ^{2} ight)(1.20 m )\left(\frac{1 kN }{1000 kg \cdot m / s ^{2}} ight)\left(\frac{1 kPa }{1 kN / m ^{2}} ight) \&=12.0 kPa\end{aligned}[/latex]

(b) To provide a gage pressure of 20 kPa at the arm level, the height of the surface of the IV fluid in the bottle from the arm level is again determined from

[latex]\begin{aligned}&P_{ ext {gage, arm }}= ho g h_{ ext {arm-bottle }} ext { to be } \&\begin{aligned}h_{ ext {arm-bottle }} &=\frac{P_{ gage , arm }}{ ho g} \&=\frac{20 kPa }{\left(1020 kg / m ^{3} ight)\left(9.81 m / s ^{2} ight)}\left(\frac{1000 kg \cdot m / s ^{2}}{1 kN } ight)\left(\frac{1 kN / m ^{2}}{1 kPa } ight) \&=2.00 m\end{aligned}\end{aligned}[/latex]

Discussion Note that the height of the reservoir can be used to control flow rates in gravity-driven flows. When there is flow, the pressure drop in the tube due to frictional effects also should be considered. For a specified flow rate, this requires raising the bottle a little higher to overcome the pressure drop.

Question 3.4: Gravity Driven Flow from an IV Bottle Intravenous infusions ...

Related Answered Questions