1 a calculate the mass flow rate in grams per second of...

(a) Calculate the mass flow rate (in grams per second) of blood (ρ = 1.0 g/cm³) in an aorta with a cross-sectional area of 2.0 cm² if the flow speed is 33 cm/s. (b) Assume that the aorta branches to form a large number of capillaries with a combined cross-sectional area of 3.0 × 10³ cm². What is the flow speed in the capillaries? cm/s 2. The approximate inside diameter of the aorta is 0.47 cm; that of a capillary is 12 µm. The approximate average blood flow speed is 1.0 m/s in the aorta and 1.0 cm/s in the capillaries. If all the blood in the aorta eventually flows through the capillaries, estimate the number of capillaries in the circulatory system.

Transcript

00:01 Hi there.

00:01 So for this problem, for the first part of this problem for part a, we are asked about to calculate the mass flow rate in grams per second of blood, which has a density that is equal to 1 gram per cubic centimeter in an aorta with a cross -ceptional area.

00:27 So the conceptional area is also given, and that is two centimeters square.

00:36 Now, if the flow speed is also given, and that is 33 centimeters per second, so the question in here is the mass flow.

00:55 So the mass flow is going to be given by the product between the density, the crop sectional area, and the speed.

01:06 So we will have that this is 1 grams per cubic centimeter times 2 centimeters square.

01:14 And this times the speed that is 33 centimeters per second.

01:19 So in here we obtain a value of 606.

01:27 Grams per second.

01:30 So that's a solution for part a of this problem.

01:35 And now for part b, we are asked about to assume that the aorta branches to form a large number of capillaries with a combined perceptional area.

01:50 So in this case, the conceptual area is also given, and that is three times 10 to the three.

02:01 Centimeters square.

02:05 So the question is what is, yes, what is the flow speed in the capillaries? so to obtain that, we use the equation of continuity that states that well, the value given we're going to call this the area prime.

02:36 So we know that the area in the aorta times the speed and then this is equal to the total area prime times this speed prime so since we want the speed prime we solve for it so we obtain this expression here and now we substitute the values remember that the area is the the one from before two centimeters square and this times the speed that we obtained from before which is 606.

03:12 Oh no, sorry, it was 33, 33, if i'm correct, and centimeters per second.

03:24 And this divided by the total area that we are given for this problem, which is 3 times 10 to the 3 centimeters square.

03:33 So using our calculator, we obtain a value of 0 .0 .0 .2.

03:46 22 centimeters per second.

03:50 That we can also write as 22 times 10 to the minus 3 centimeters per second.

04:01 So that's the solution for part b of this problem...

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