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KatieKT
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We will construct a simple model of the circulatory system to investigate the rate at which cuts bleed. In this model we will assume that blood is a Newtonian fluid at all length scales so that the equations of fluid flow which we have been studying will apply. We will also assume that the effects of viscosity may be ignored.
A large artery has a diameter of 7mm and carries blood which flows with a peak velocity of 0.15 m s−1. This vessel eventually feeds a network of capillaries which together have an area approximately 400 times that of the large artery which feeds into them. In this model, the capillaries are identical to each other and have a diameter of 7.5 μm.
(a) Suppose that the diastolic blood pressure is 130 mmHg at the level of the heart and the blood velocity in the large artery at the heart is 0.15 m s−1. What is the blood velocity in the artery at a point 1 m below the heart? (The density of blood is 1050 kg m−3).
(b) If the artery is severed at a at a point 1m blowthe heart, what is the maximum velocity of blood flow from the artery?
(c) What is the blood velocity in a capillary in the capillary net at this point (1m below the heart)?
(d) What is the blood pressure in the capillary net at this point (in mmHg and with the assumptions discussed above)?
(e) If a capillary is severed, what is the blood velocity leaving the wound? (again on the basis of this model)
Related Formulas- P+1/2 pv² + pgh
Attempted Solution:
A)Constant = P+1/2 pv² + pgh
= 17.32 + 1/2(1050)(.15)² + (1050)(-9.81)(1)
=17.32 + .118 - 10.3
= 7.138m/s
Or my other solution is:
A1V1= A2V2
V2= A1V1/A2
= ((∏0.0035²)(0.15))/ ∏0.000375²
=13.06m/s
I'm thinking that these are the two ways to solve A) but why are they not the same ansewr? Should I use one formula instead of the other?
A large artery has a diameter of 7mm and carries blood which flows with a peak velocity of 0.15 m s−1. This vessel eventually feeds a network of capillaries which together have an area approximately 400 times that of the large artery which feeds into them. In this model, the capillaries are identical to each other and have a diameter of 7.5 μm.
(a) Suppose that the diastolic blood pressure is 130 mmHg at the level of the heart and the blood velocity in the large artery at the heart is 0.15 m s−1. What is the blood velocity in the artery at a point 1 m below the heart? (The density of blood is 1050 kg m−3).
(b) If the artery is severed at a at a point 1m blowthe heart, what is the maximum velocity of blood flow from the artery?
(c) What is the blood velocity in a capillary in the capillary net at this point (1m below the heart)?
(d) What is the blood pressure in the capillary net at this point (in mmHg and with the assumptions discussed above)?
(e) If a capillary is severed, what is the blood velocity leaving the wound? (again on the basis of this model)
Related Formulas- P+1/2 pv² + pgh
Attempted Solution:
A)Constant = P+1/2 pv² + pgh
= 17.32 + 1/2(1050)(.15)² + (1050)(-9.81)(1)
=17.32 + .118 - 10.3
= 7.138m/s
Or my other solution is:
A1V1= A2V2
V2= A1V1/A2
= ((∏0.0035²)(0.15))/ ∏0.000375²
=13.06m/s
I'm thinking that these are the two ways to solve A) but why are they not the same ansewr? Should I use one formula instead of the other?
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