Flow Velocity of Blood Conceptual Question

Arteriosclerotic plaques forming on the inner walls of arteries can decrease the effective cross-sectional area of an artery. Even small changes in the effective area of an artery can lead to very large changes in the blood pressure in the artery and possibly to the collapse of the blood vessel.

Imagine a healthy artery, with blood flow velocity of v0=0.14m/s and mass per unit volume of ρ=1050kg/m3. The kinetic energy per unit volume of blood is given by

K
=`(1/2)pv^2

PART A
Compared to normal blood flow velocity, v0, what is the velocity of blood as it passes through this blockage?

PART B
By what factor does the kinetic energy per unit of blood volume change as the blood passes through this blockage?








PART C
As the blood passes through this blockage, what happens to the blood pressure?









PART D
Relative to its initial, healthy state, by what factor does the velocity of blood increase as the blood passes through this blockage?








PART E
By what factor does the kinetic energy per unit of blood volume increase as the blood passes through this blockage?






PART F
What is the magnitude of the drop in blood pressure, Δp, as the blood passes through this blockage? Use K0 as the normal (i.e., unblocked) kinetic energy per unit volume of the blood.

Submerged Block

A beaker contains a thick layer of oil (shown in green) of density ρ2 floating on water (shown in blue), which has density ρ3. A cubical block of wood of density ρ1 with side length L is gently lowered into the beaker, so as not to disturb the layers of liquid, until it floats peacefully between the layers, as shown. (Figure 1)

What is the distance d between the top of the wood cube (after it has come to rest) and the interface between the oil and water?

Submerged Sphere in a Beaker

Submerged Sphere in a Beaker

A cylindrical beaker of height 0.100m and negligible weight is filled to the brim with a fluid of densityρ = 890kg/m3 . When the beaker is placed on a scale, its weight is measured to be 1.00N .(Figure 1)

A ball of density ρb = 5000kg/m3 and volumeV = 60.0cm3 is then submerged in the fluid, so that some of the fluid spills over the side of the beaker. The ball is held in place by a stiff rod of negligible volume and weight. Throughout the problem, assume the acceleration due to gravity is g = 9.81m/s2 

PART A

What is the weight Wb of the ball?

ANSWER = 2.94 N

PART B

What is the reading W2 of the scale when the ball is held in this submerged position? Assume that none of the water that spills over stays on the scale.

ANSWER = 1.00 N

PART C

What is the force Fr applied to the ball by the rod? Take upward forces to be positive (e.g., if the force on the ball is downward, your answer should be negative).

ANSWER = 2.42 N

PART D

What weight W3 does the scale now show?

ANSWER = 3.42 N