Blood is pumped through a large artery of a man lying on the ground working unde
ID: 2992728 • Letter: B
Question
Blood is pumped through a large artery of a man lying on the ground working under an automobile. The blood discharges through a cut through the artery into the atmosphere with an unknown flow speed. The heart (a pump) has a head of 10 feet. A heart valve in the flow path has a value of KL = 10. The pressure just upstream of the heart is 80 mm Hg. (artery length = 2 ft. from the heart to the cut, diameter = 0.1 in., and ? = 0.001 in.) Calculate the flow speed at the cut and determine if this is a reasonable value based on your appropriate research. (SG=1, ? = 4 x 10-3 N-s/m2)Explanation / Answer
/d = 0.001/0.1 = 0.01
Re = Vd/ = 1000*V*(0.1*0.0254)/(4*10^-3) = 635*V
Head loss h = fL/d*V^2/2g = f(2*12/0.1)*V^2/2g = 12.232*fV^2
Assuming laminar flow, f = 64/Re = 64/(635*V) = 0.1/V
h = 12.232*(0.1/V)*V^2 = 1.2232*V
(80/1000)*13.6 = -(10*12*0.0254) + 10*(V^2/2g) + 1.2232*V
0.51*V^2 + 1.2232*V - 4.136 = 0
Solving this gives, V = 1.89 m/s
(So, Re = 635*1.89 = 1200 which is <2300. Hence, assumption of laminar flow is valid.)