One method to estimate the flow rate of blood delivered by the heart (called the

Question

One method to estimate the flow rate of blood delivered by the heart (called the "cardiac output") is to continuously inject a dye into the artery (aorta) entering a part of the circulatory system called the "systemic circulation" and measure the dye concentration in the outlet from that systemic circulation. So the systemic circulation has two inlets - the blood and dye streams (the inlet blood stream contains no dye) - and a single combined outlet stream. In one such measurement, the dye is injected at a rate of 20 g/min, and the measured dye content in the outlet is, 0.39 wt%. What is the mass flow rate of blood and dye exiting the 1 systemic circulation? What is the mass flow rate of just the blood through the systemic circulation (without the dye)? If the density of blood is 1.06 g/cm^3, what volumetric flow rate is indicated by the answer to part (b)?

Explanation / Answer

Solution:

Dye flow rate + Blood flow rate = Combined stream flow rate

Basis = 1 min

Let the blood quantity pumped per hour = x g/min

So in one hour the total Qty of blood = x g

Total dye injected in 1 min = 20 g/min x 1 min = 20 g

The mass balance is,

Total dye / (Total blood + Total dye) = 0.39 % wt/wt

20 / (x + 20) = .0039

x = 5108.205 g/min

a) Mass flow rate of blood and dye = 5108.25 + 20 = 5128.25 g/min

b) Mass flow rate of blood = 5108.205 g/min

c) Volumetric flow rate of blood = mass flow rate of blood/ density of blood =

(5108.205 g/min) / 1.06 g/cm^3 = 4819.06 cm^3/min

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.