Question

The velocity of blood in a blood vessel of 2.0 cm radius is 30 cm/s. When the blood vessel bifurcates into 2 smaller vessels of radius 1.0 cm each, the velocity of blood in each of the smaller vessels is ______ cm/s. Assume vessel walls are rigid, and blood is incompressible.

Hint:

For incompressible fluids: $A_1 v_1 = \sum A_i v_i$. If one vessel splits into $n$ equal smaller ones, each velocity scales inversely with area ratio.

Answer 1

Correct Answer: 60

Step 1: Apply the principle of continuity. 
For incompressible flow: \[ A_1 v_1 = 2 A_2 v_2 \] where $A = \pi r^2$. 
Step 2: Substitute values. 
\[ \pi (2)^2 (30) = 2 \pi (1)^2 v_2 \] \[ 4 \times 30 = 2 v_2 \] \[ v_2 = 60~\text{cm/s} \] Wait—carefully: 
We should check factorization: \[ 4 \times 30 = 2(1)^2 v_2 \Rightarrow v_2 = 60 \] Thus, the velocity in each smaller vessel = 60 cm/s.
 If asked in cm/s (consistent rounding): \[ \boxed{v_2 = 60~\text{cm/s}} \]