The blood speed in a normal segment of a horizontal artery is 0.166 m/s. An abnormal segment of the artery is narrowed down by an arteriosclerotic plaque to 1/5 of its normal cross-sectional area. What is the difference in blood pressure between the normal and constricted segments of the artery?
1/5 of the area ----> 5 times the speed
if the same amount passes each point in a second (continuity)
p + (1/2) rho v^2 = constant says Mr Bernoulli
P1 + (1/2) rho v^2 = P2 + (1/2) rho (5 v)^2
P1 - P2 = (1/2) rho (25-1)v^2
rho is approximately that of water 1000 kh/m^3
and v is .166 m/s
so
P1-P2 = 500 (24)(.166)^2
Thanks! blood's density is 1060 kg/m^3 but it worked perfectly! and makes sence
To determine the difference in blood pressure between the normal and constricted segments of the artery, we can use the principle of conservation of mass and the Bernoulli's equation.
Step 1: Calculate the flow rate
The flow rate (Q) of blood remains constant between the normal and constricted segments of the artery. It can be calculated using the formula:
Q = A * V
Where:
Q = Flow rate
A = Cross-sectional area of the artery
V = Blood speed
Given that the blood speed in the normal segment of the artery is 0.166 m/s, and the cross-sectional area in the narrowed segment is reduced to 1/5 of its normal size, we can calculate the cross-sectional area in the abnormal segment as follows:
A_narrowed = (1/5) * A_normal
Step 2: Calculate the pressure difference using Bernoulli's equation
Bernoulli's equation relates the pressure difference (∆P) to the velocity of the fluid. It states that:
∆P = (1/2) * ρ * (∆V)^2
Where:
∆P = Pressure difference
ρ = Density of the fluid (assumed to be constant for blood)
∆V = Change in velocity between the two segments
Step 3: Calculate the change in velocity (∆V)
The change in velocity (∆V) between the normal and constricted segments can be calculated using the equation:
∆V = V_normal - V_narrowed
Substituting the given values, we have:
∆V = 0.166 m/s - V_narrowed
Step 4: Substitute values and calculate the pressure difference
Plug in the values we have into the equation for the pressure difference:
∆P = (1/2) * ρ * (∆V)^2
Finally, you can calculate the pressure difference (∆P) by substituting the numerical values you have obtained.
Remember to use the appropriate units consistently throughout the calculation (e.g., SI units for length, area, velocity, and pressure).