Question

FLUIDS QUESTION
?Blood from a supine patient flowing through the internal carotid artery is measured to be

2. Blood from a supine patient flowing through the internal carotid artery is measured to be 42.6 cm/s. The base of the artery measures 4.85 mm and the blood pressure at this point is 92.56 mmHg. There is an aneurysm in the vessel with a diameter measuring 16.1 mm. The density of the patient's whole blood was determined to be 1.04 x 103 kg/m3. Assuming inviscid flow (in large diameter vessels) and no hydrostatic effects, determine the following: (20 pts) a. Given the questions below (b-d), state the fluid flow assumptions that you will use to b. Make a sketch/diagram of the model system and label it according to the system parameters What is the average velocity (cm/s) of blood flow in the aneurism region? What is the blood pressure (kPa) in the aneurism? c. d.

42.6 cm/s. The base of the artery measures 4.85 mm and the blood pressure at this point is

92.56 mmHg. There is an aneurysm in the vessel with a diameter measuring 16.1 mm. The

density of the patient’s whole blood was determined to be 1.04 x 10

3

kg/m

3

. Assuming

steady-state, inviscid flow (in large diameter vessels) and no hydrostatic effects, determine

the following

Answer 1

Given: - V_1 = 426 cm/s d_1 = 4.85 mm = 0.485 cm p_1 = 92.56 mm Hg = 9.256 cm Hg S = 1.04 times 10^3 kg/m^3 = 1.04 times 10^3 kg/cm^3 d_2 = 16.1 mm = 1.61 cm a) Assumption - Flow is frictionless Fluid is incompressible Velocity is uniform over cross section c) Q_1 = Q_1 A_1 V_1 = A_2 V_2 phi/4 0.485^2 times 42.6 = phi/4 times 1.61^2 V_2 V_2 = 3.86 cm/s \r\n d) p_1 = 9.256 cm Hg p_1 = 13600 times 10^-6 times 98.1 times 9.256 ....... (p = 5 _Hg gh) = 12.34 Kpa = 12.34 times 10^3 N.m^2 By using Bemoullis theorem g Z_1 + p_1/5 + V^2_1/2 = g Z_2 + p_z/5 + V^2_1/2 Z_1 = Z_2 .....(patient is supine) therefore p_1/5 + V^2_1/2 = p_2/5 + V^2_2/2 12.34 times 10^3/1.04 times 10^3 + 4.26^2/2 = p_2/1.04 times 10^3 + 0.386^2/2 11.865 + 9.0738 = p_2/1.04 times 10^3 + 0.0744g