Plaque builds up on the walls of an artery decreasing its diameter from 1.16 cm
ID: 1421205 • Letter: P
Question
Plaque builds up on the walls of an artery decreasing its diameter from 1.16 cm to 0.62 cm. If the flow speed is 13.0 cm/s before reaching the region of plaque buildup, determine the following. (a) speed at which blood is traveling through the plaque-constricted regioncm/s
(b) pressure change within the plaque-constricted region. (Assume the density of blood is 1050 kg/m3. Be sure to include the appropriate sign with your answer.)
Pa Plaque builds up on the walls of an artery decreasing its diameter from 1.16 cm to 0.62 cm. If the flow speed is 13.0 cm/s before reaching the region of plaque buildup, determine the following. (a) speed at which blood is traveling through the plaque-constricted region
cm/s
(b) pressure change within the plaque-constricted region. (Assume the density of blood is 1050 kg/m3. Be sure to include the appropriate sign with your answer.)
Pa (a) speed at which blood is traveling through the plaque-constricted region
cm/s
(b) pressure change within the plaque-constricted region. (Assume the density of blood is 1050 kg/m3. Be sure to include the appropriate sign with your answer.)
Pa
Explanation / Answer
Continuity for fluid flows gives us rho*A*V = constant. Assuming no density change we have
A1*V1 = A2*V2 so V2 = A1/A2*V1 = pi*(1.16/2)^2/pi*(0.62/2)^2*13cm/s = 26.92cm/s
From Bernoulli's eqn with no height change we have
p1 + 1/2*rho*V1^2 = p2 + 1/2*rho*V2^2 So pressure drop = p1 - p2 = 1.2*rho*(V2^2 - V1^2)
[note change units to kg & m/s so the answer will be in Pa]
= 1/2*1050kg/m^3*((.269m/s)^2 - (.13m/s)^2) = 29.11Pa