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In Deriving Bernoulli’S Equation, We Equated the Work Done on the Fluid in the Tube to Its Change in the Potential and Kinetic Energy. (A) What is the Largest Average Velocity of Blood Flow in an Artery of Diameter 2 × 10–3 M If the Flow Must Remain Laminar? (B) Do the Dissipative Forces Become More Important as the Fluid Velocity Increases - CBSE (Science) Class 11 - Physics

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Question

In deriving Bernoulli’s equation, we equated the work done on the fluid in the tube to its change in the potential and kinetic energy. (a) What is the largest average velocity of blood flow in an artery of diameter 2 × 10–3 m if the flow must remain laminar? (b) Do the dissipative forces become more important as the fluid velocity increases? Discuss qualitatively.

Solution 1

a) 1.966 m/s 

Diameter of the artery, d = 2 × 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 as:

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

`= (2000xx2.084xx 10^(-3))/(1.06xx10^3xx2xx10^(-3))`

= 1.966 m/s

Therefore, the largest average velocity of blood is 1.966 m/s.

b)Yes

As the fluid velocity increases, the dissipative forces become more important. This is because of the rise of turbulence. Turbulent flow causes dissipative loss in a fluid.

Solution 2

(a) If dissipative forces are present, then some forces in liquid flow due to pressure difference is spent against dissipative forces, due to which the pressure drop becomes large.

(b) The dissipative forces become more important with increasing flow velocity, because of turbulence.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Physics Textbook for Class 11 (2018 to Current)
Chapter 10: Mechanical Properties of Fluids
Q: 25 | Page no. 271
Solution In Deriving Bernoulli’S Equation, We Equated the Work Done on the Fluid in the Tube to Its Change in the Potential and Kinetic Energy. (A) What is the Largest Average Velocity of Blood Flow in an Artery of Diameter 2 × 10–3 M If the Flow Must Remain Laminar? (B) Do the Dissipative Forces Become More Important as the Fluid Velocity Increases Concept: Bernoulli’S Principle.
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