43. The heart of a typical person pumps 5 L per minute of blood into the aorta.

Question

43. The heart of a typical person pumps 5 L per minute of blood into the aorta. This equates to a volume flow rate of 8.3x10 ms a) Explain the equation of continuity, using a diagram if you wish. (3 marks) b) What is the speed of blood in the aorta, assuming it has an inner diameter of 2.2 cm? (3 marks) After travelling through the aorta, the blood vessels branch out, and eventually the blood reaches the capillaries. What is the speed of blood flow in the capillaries, assuming a total cross-sectional area of 3500 cm2 summed over all the capillaries? (3 marks) c)

Explanation / Answer

43. a) Equation of Continuity: It is based on "Law of Conservation of Mass", it stats that fluid passing through a tube in a steady flow, the mass flowing through any section of tube per unit time is constant.

consider a tube of two different diameters (one wider than the other), according to the conservation of mass what comes in through one end of the tube must go out, the flow rate in the wider section must same as the flow rate in the smaller section.

The flow of liquid follows pressure gradient (liquid flows from high pressure to low pressure in the tube

?1 = flow rate 1=?2 = flow rate 2

or

A1v1=A2v2 where A1 =cross sectional area at point 1,v1=flow velocity at point 1.

A2 =cross sectional area at the point 2, v2=flow velocity at the point 2.   

b)Flow rate (Q)=Volume(V)/Time(t) {volume=Area(A)*lenght(l)}

=(A*l)/t

=A*v {speed(v)=distance(l)/t}

area of a cylinder (=blood vessel)=pi*radius(r)2=3.14*1.12 {pi=3.14 or 22/7,diameter =radius/2=2.2/2=1.1}

=3.7994 cm2.

v=Q/A=8.3*10-5/3.7994*10-4 {1cm2=1*10-4m2}

=0.2185 m/s.

c) we use the formula A1V1=A2V2

3.7994 cm2.* 0.2185 m/s.=3500 cm2*V2 {A1(from previous answer)=3.7994 cm2,V1(from previous answer)= 0.2185 m/s}

V2=.2.37*10-4m/s.

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

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