What is the pressure difference required to make blood flow through artery of inner radius 2.0 mm and length 0.18 m at a speed of 5.6 cm/s?
I used P1-P2 = speed*8*n*L/r squared
n = viscosity of blood = 4 x 10e-3
L = .18 m
r = 2 x 10e-3 m
When plugged in I get P1-P2 - 80.64 Pa but this is wrong! Help!
To determine the pressure difference required to make blood flow through an artery, we can use the Poiseuille's Law equation you mentioned. However, it seems like there might be a mistake in your calculations. Let's go through the equation step by step and double-check the calculations.
The equation you used is:
P1 - P2 = (8 * n * L * V) / (π * r^4)
Where:
P1 - P2 is the pressure difference
n is the viscosity of blood (4 x 10^-3 Pa·s)
L is the length of the artery (0.18 m)
V is the velocity of blood flow (5.6 cm/s = 0.056 m/s)
r is the radius of the artery (2.0 mm = 0.002 m)
Plugging in these values, the corrected equation becomes:
P1 - P2 = (8 * (4 x 10^-3) * 0.18 * 0.056) / (π * (0.002)^4)
Now let's perform the calculations step by step:
Step 1: Calculate the radius squared:
(0.002)^4 = 0.0000000016
Step 2: Multiply the numerator:
8 * (4 x 10^-3) * 0.18 * 0.056 = 0.000019648
Step 3: Divide the numerator by the denominator:
0.000019648 / (π * 0.0000000016) ≈ 38812.424
Therefore, the pressure difference (P1 - P2) required to make blood flow through the artery is approximately 38812.424 Pa or 38.8 kPa.
Make sure to check your calculations and units carefully to avoid any errors. Let me know if there's anything else I can help you with!