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The pressure drop along a length of artery is 125 Pa, the radiusis 15 mm, and the flow is laminar. The average speed of the bloodis 12 mm/s.a) 8.83x10^-2b) What is ...

Question

The pressure drop along a length of artery is 125 Pa, the radiusis 15 mm, and the flow is laminar. The average speed of the bloodis 12 mm/s.a) 8.83x10^-2b) What is the power (in mW) expended maintaining the flow?

The pressure drop along a length of artery is 125 Pa, the radius is 15 mm, and the flow is laminar. The average speed of the blood is 12 mm/s. a) 8.83x10^-2 b) What is the power (in mW) expended maintaining the flow?



Answers

The pressure drop along a length of artery is 100 Pa, the radius is 10 mm, and the flow is laminar. The average speed of the blood is 15 mm/s. (a) What is the net force on the blood in this section of artery? (b) What is the power expended maintaining the flow?

So given the radius off the arteries and the density because we know the temperature. We also know the viscosity at that temperature, which which is which is for blood to 0.84 Millie passport. Second, we want to find out the corresponding velocity for which the flow is lambda. So laminar flow needs 2000 are smaller, that's number. And if you remember, very formula for eons. Number is Turo. Are we by Peter? So this needs to be less than 2000 which means our I'm sorry. The velocity needs to be less than 2000 Kita divided by Turo. I think that's that. So we'll find this number 2000 times. Eater is 2.84 into environments Tree he rented a two times rule is one point 10 to 5 times radius is two millimeters. So that's two into 10 by ministry. This chance. So do we. But 1.2 meter per second. So we lost. He needs to be less than 1.2 meters per second. So what is the corresponding volume? Read off, Luke, That is simply the last two times Pi r square, the service, a theater of cross section. So that's one point stiletto you pie in tow to entertain part minus three Whole square, which turns out to be 1.8 into four, minus two. Leader for seconds complicity.

In this problem we are given the speed of blood in a 31 is equal to 2.65 centimetre per second. And the damage of This artery is 1.4 millimeter, which is a good too. Their .14 centimetre and the director of smaller arteries 1.36 mm, Which is equal to 0.136. Saint Peter. We're asked to find the speed in the small laboratory is from equation of continuity florid must be good. Which is and when we went is equal to A to B two. When we hear in this question for we too we get we do has got to Even we will do it by a two which is equal to by divan squared right before we even do it by pi The two squared divided by four which is equal to do you want square Run by 22 square. Built it that way. Even so we will subsidiaries V two is equal to The one is their .14 centimeter square, divided by Ditto is equal to 0.136 centimeter square. We'll keep that by Women is equal to 2.65 sent you deeper skin. When we saw this, forget we Two is equal to two point 8 1 sent you to per skill is the answer to this question. Thank you for watching with you.

And we have release of artery R one equals to one cm and R two equals to 0.3 cm. And Velocity V one of the blood flow Is 0.4 m/s. So applying continued equation at one and two we get U. Equals two. A. V. area of the velocity. That is by our one square. We won equals to buy our to spare manipulable. So from here we get we do equals two Are won by our two square multiplied by we want. So substituting the values we get Wonder Where by 0.3 Holy Square Multiplied by 0.4 m/s. So from here after solving the two comes out to be 4.44 m/s. So this is the answer for the part of the problem. Okay, this is a part now moving to the party in which we have to determine the gates pressure at this second. But okay, so playing Bernoulli equation to the system, we can write Caven plus huge. Even plus even minus P two equals two K two plus you. Ok Kay is potential energy and huge. Is gravitational energy. So we can write given plus he wrote Plus even -12 equals two K two plus zero potential energy is zero at the position because it is on horizontal level. So Kevin will be called stolen by two row. Even is square plus even minus P two equals to kato will be won by two roe V two square. Okay, so now from here we can try it even minus people Even -22 Well equals to combine to roll way to square minus we even square. So no the density rho is equal to 1050 program per meter cubed Which is density of blood. So now substituting the values we have even equals to 1.4. multiplied by 10 to the power four minus people equals two. one x 2 x. 105.0 Baby two is 4.44 which is obtained in the part a. And we one is 0.4 which is given in the question. So from here after solving We get paid to equals to 3.7. But that weight into the power four newton per military square. So this will be equals two B two equals two 0.37 bar. Okay. 3 7. But so this is our gaze question. Okay, this is the gives pressure. So this is the answer for the question. Okay, this is people. Okay. We can rewrite it for more clarity people. So this is the answer. Okay.

All right, So we've got some blood going along. We're gonna play magnetic field and German. The velocity. Average speed of the blood. We have the hall voltage, too. So the hall voltage is equal to the drift. Velocity tends the magnetic field times the diameter hall. Voltage is 88 my girl. So to the negative six, the votes magnetic field is 0.115 test lows. The diameters 3.8 millimeters Does he sent Emily moving three times 123 So 1230.0 zero 38 meters. All right, divide by those to you. End up with a velocity of 0.2. Looks like through three significant figures. 01 meters per second.


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