Question

A section of blood vessel wall has become weakened resulting in an increase in the vessel wall diameter of 32%.

For this question treat blood as an incompressible non viscous fluid of density 1050 kg m−3. If the vessel normally carries blood at a speed of 1.2 m s−1 then what is the magnitude of the increase in pressure in the bulge in the blood vessel? (to 2 s.f and in Pa)

Answer 1

$$A_1v_1=A_2v_2\to d_1^2v_1=d_2^2v_2$$

According to Bernoulli's equation:

$$Δp=p _2 ​ −p _ 1 ​ =0.5\rho (v_1^2-v_2^2)=0.5\rho v_1^2\left(1-\left(\frac{d_1}{d_2}\right)^4\right)$$

$$Δp=0.5(1050)(1.2)^2\left(1-\left(\frac{1}{1+0.32}\right)^4\right)=507\ Pa$$