Download Suppose that a 70 kg stature is at the bottom of a lake. The stature

Suppose that a 70 kg stature is at the bottom of a lake. The
stature has a volume of 3x104 cm3. How much force is needed
to lift the stature at constant velocity?
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FL
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In working out his principle, Pascal showed dramatically how force
can be multiplied with fluid pressure. Suppose that you want to
reproduce his experiment and you place a long thin tube of 0.30 cm
radius vertically into a 20 cm radius barrel of Jack Daniels Whiskey.
You find that when the barrel was filled with water (no one wants to
waste the JD) and the tube filled to a height of 12 m, the barrel burst.
What are the mass of fluid in the tube and the net force on the barrel
lid?
A 5/8 inch diameter hose is used to fill a round swimming pool 7.2 meters
in diameter. How long will it take to fill the pool to a depth of 1.5 m if the
water flows out of the hose at a rate of 0.28 m/s?
An example of Bernoulli's equation:
Consider the airplane shown below. What is the aerodynamic
lift (in Newtons) produced on the wing if the wing has a 60m2
surface area and the velocity of the wind on the top and
bottom of the wing are 340 m/s and 290 m/s respectively?
In the old west, a desperado fires a bullet into an open water tank
creating a hole at a distance h = 5m below the water surface (which is
open to the air). What is the speed of the water emerging from the hole?
Bernoulli’s principle can be applied to a syringe to describe the
dynamics of an injection. If position 1 is within the body of the syringe
and 2 is within the needle, derive an expression for the velocity of the
fluid exiting the needle.
If the body of the syringe above is held horizontally has a cross sectional
area of 2.5x10-5 m2 and the needle has a cross sectional area 1x10-8 m2.
Suppose a force of 2 N is applied to the plunger to eject the medicine,
what is the speed of the fluid as it leaves the needle’s tip? (Hint: in the
absence of the force, the pressure on the syringe is 1 Atm.)
Suppose that the pressure in the cerebrospinal fluid (CSF) is measured as
shown below, using a spinal tap with the patient sitting erect. The pressure
due to the weight of the CSF (given that its density is 1050 kg/m3) in the spinal
column increases the pressure.
a.What is the pressure measured in Pascal if the pressure around the brain is
10mm Hg and the tap is at a point 60cm lower than the brain?
b. What is the pressure measured in Pascal and in centimeters of water if the
person is lying down?
Suppose that the aorta has a radius of about 1.25cm and that the typical blood
velocity is around 30 cm/s and that it has an average density of 1060 kg/m3.
a. What is the average blood velocity in the major arteries if the total cross
sectional area of the major arteries is 20cm2?
b. What is the total flow rate?
c. On the assumption that all the blood in the circulatory system goes through
the capillaries, what is the total cross sectional area of the capillaries if the
average velocity of the blood in the capillaries is 0.03cm/s?
d. If a typical capillary has a cross sectional area of 3x10-11 m2, about how
many capillaries are there in the human body?
e. What are the kinetic energy per unit volume for blood in the aorta, the
major arteries, and the capillaries?
f. If a capillary has an average length of 0.75mm what is the average time that
a red blood cell remains in a capillary?