# What is the Largest Average Velocity of Blood Flow in an Artery of Radius 2 × 10–3 M If the Flow Must Remain Laminar? (B) What is the Corresponding Flow Rate - Physics

#### Question

(a) What is the largest average velocity of blood flow in an artery of radius 2 × 10–3 m if the flow must remain laminar? (b) What is the corresponding flow rate? (Take viscosity of blood to be 2.084 × 10–3 Pa s).

#### Solution 1

a)

Radius of the artery, r = 2 × 10–3 m

Diameter of the artery, d = 2 × 2 × 10–3 m = 4 × 10– 3 m

Viscosity of blood, eta = 2.084 xx 10^(-3) Pas

Density of blood, ρ = 1.06 × 103 kg/m3

Reynolds’ number for laminar flow, NR = 2000

The largest average velocity of blood is given by the relation:

V_"arg" = (N_Reta)/(rhod)

= (2000xx2.084xx10^(-3))/(1.06xx10^3xx4xx10^(-3))

= 0.983 m/s

Therefore, the largest average velocity of blood is 0.983 m/s.

b) Flow rate is given by the relation:

R = pir^2V_"arg"

= 3.14 xx (2xx10^(-3))^2 xx 0.983

= 1.235 xx 10^(-5) m^3 s^(-1)

Therefore, the corresponding flow rate is 1.235 xx 10^(-5) m^3 s^(-1)

#### Solution 2

Here r = 2 xx 10^(-3) m; D = 2r = 2xx2xx10^(-3) =  4xx 10^(-3) m

eta = 2.084 xx 10^(-3) Pa-s; rho = 1.06 xx 10^3 kg m^(-3)

For flow to be laminar , N_R = 2000

a) Now v_c = (N_Reta)/rho_D = (2000xx(2.084xx10^(-3)))/((1.06xx10^3)xx(4xx10^(-3))) = 0.98 "m/s"

b)Volume flowering per second  =pir^2v_c = 22/7 xx (2xx10^(-3))^2 xx 0.98 = 1.23 xx 10^(-5) m^3s^(-1)

Is there an error in this question or solution?

#### APPEARS IN

NCERT Solution for Physics Textbook for Class 11 (2018 (Latest))
Chapter 10: Mechanical Properties of Fluids
Q: 26 | Page no. 271

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What is the Largest Average Velocity of Blood Flow in an Artery of Radius 2 × 10–3 M If the Flow Must Remain Laminar? (B) What is the Corresponding Flow Rate Concept: Viscosity.