Tutorial FLUID

For STUDENT

Q1 A swimming pool is 5 meters deep and measures 12 x 20 meters. What is the pressure at the

bottom, and the total force is exerted on the pool bottom by the water?

Q2 An irregularly shaped pool has slanted walls so that the volume of water in it is difficult to

determine. Its depth is measured to be 3 meters. How could you calculate the hydrostatic

pressure at the bottom of the pool?

Q3 The systolic blood pressure is 120 mmHg. What is the pressure in pascals and lb/in2 ?

Q4 The radius of the aorta is 0.9 cm, with the average flow speed is 32.8 cm/sec. What is the

volume flow rate of blood? What is the speed of blood flow in capillaries if they have

diameter as small as 10 micrometers.

Q5 If a capillary has a radius of 2x10-4cm and the average velocity of flow through it is 0.03 cm/s.

what is the volume flow rate through the capillary? If the flow rate through the aorta is

80cm3/s, how many such capillaries would be required to carry the total blood flow?

Q6 Suppose a normal coronary artery has a volume flow rate of 100 cm3/min. when the person’s

average blood pressure is 100 mmHg. Calculate the flow rates if the internal radius of that

artery is reduced to 80% of its normal value. If all blood vessels were similarly affected, what

blood pressure would be required to restore the normal volume flow rate of 100 cm3/min.

Q7 If dry air at pressure of 100 000 Pascal is 78.09% nitrogen, 20.95% oxygen, 0.93% argon and

0.03% carbon dioxide (by amount), what is partial pressure of each component? The sum of

partial pressure is equal to the total pressure of the mixture.

Q8 Fight regulation usually require the provision of artificial oxygen supplies for operation above

about 3000 meters. Compare the amount of oxygen available per breath at this altitude (total

pressure 70 000 Pa, temperature 279K) with that available at sea level.

Q9 The pressure in the aorta is 100 mmHg & a radius 0.9cm. What is the wall tension in the aorta?

Q10 Isolated alveoli in lungs are kept inflated to a radius of 0.15 mm by an internal pressure 4

mmHg higher than that outside the alveoli. What is the surface tension of the surfactant-

containing fluid that coats the alveoli? Assume spherical alveoli.

Tutorial FLUID

Q1 A swimming pool is 5 meters deep and measures 12 x 20 meters. What is the pressure

at the bottom, and the total force is exerted on the pool bottom by the water?

A1 The water pressure at the bottom is P=ρ g h=(1000 kg/m3)(9.8 m/s2)(5m)=49 000 N/m2

The total force F = P x A = (49 000 N/m2) (12x20 m2) = 11,760,000 N

Q2 An irregularly shaped pool has slanted walls so that the volume of water in it is

difficult to determine. Its depth is measured to be 3 meters. How could you calculate

the hydrostatic pressure at the bottom of the pool?

A2 The liquid pressure at the bottom is determined solely by the depth and density. The

total volume, total weight and shape of pool are not directly relevant.

The density of water is ρ = 1 gr/cm3 = 1000 kg/m3

Therefore P = ρ g h = (1000 kg/m3)(9.8 m/s2)(3m) = 29 400 N/m2 = 29 400 pascals

Q3 The systolic blood pressure is 120 mmHg. What is the pressure in pascals and lb/in2 ?

A3 760 mmHg = 101 325 pascals

120 mmHg = 15,960 pascals = 16 KPa = 2.3 lb/in2

Remember : 1 mmHg = 133 pascals = 0.0193 lb/inc2 = 0.00132 atmosphere

Q4 The radius of the aorta is 0.9 cm, with the average flow speed is 32.8 cm/sec. What is

the volume flow rate of blood? What is the speed of blood flow in capillaries if they

have diameter as small as 10 micrometers.

A4 The volume flow rate V = A v = (π)(0.9 cm)2(32.8 cm/s) = 83.4 cm3/s = 5 liters/min

The blood flow in capillaries have speed v = V/A = (83.4 cm3/s)/{(3.14)(5x10-4cm)2}

=1.06 x 108 cm/s

Q5 If a capillary has a radius of 2x10-4cm and the average velocity of flow through it is

0.03 cm/s. what is the volume flow rate through the capillary? If the flow rate through

the aorta is 80 cm3/s, how many such capillaries would be required to carry the total

blood flow?

A5 The volume flow rate in capillary is V = A v = (3,14)(2x10 -4cm)2 (0.03 cm/s) = 0.3768x

10-8 cm3/s. The number of capillaries are = 80/0.3768x10-8 = 2.12 x 1010

Q6 Suppose a normal coronary artery has a volume flow rate of 100 cm3/min. when the

person’s average blood pressure is 100 mmHg. Calculate the flow rates if the internal

radius of that artery is reduced to 80% of its normal value. If all blood vessels were

similarly affected, what blood pressure would be required to restore the normal volume

flow rate of 100 cm3/min.

Tutorial FLUID

A6 The Poiseuille’s law

Effect on radius = (0.8r)4 = 0.41 r4.

Effect on volume flow rate : V = (0.41) (100 cm3/min.) = 41 cm3/min.

To restore a normal volume flow rate, it has to divide the pressure by the factor 0.41 to

overcome the effect of the radius reduction, so P = (100mmHg)/(0.41) = 244 mmHg.

This is a dangerously high blood pressure.

With significantly greater reduction in radius, restoration to normal volume flow rates by

increased blood pressure is not physiologically possible.

Q7 If dry air at pressure of 100 000 Pascal is 78.09% nitrogen, 20.95% oxygen, 0.93%

argon and 0.03% carbon dioxide (by amount), what is partial pressure of each

component? The sum of partial pressure is equal to the total pressure of the mixture.

A7 Let n be the total amount of air present. Then the amount of N2 is 0.7809 n, O2 is 0.2095 n,

Ar is 0.0093 n, and CO2 is 0.0003 n.

Since the partial pressure Pi = niRT/V. The partial pressure of the various gases will be: N 2 =

78 kPa, O2 = 21 kPa, Ar = 0.9 kPa CO2 = 30 Pa

These pressures add to give the total pressure 1 x 105 Pa.

Q8 Fight regulation usually require the provision of artificial oxygen supplies for operation

above about 3000 meters. Compare the amount of oxygen available per breath at this

altitude (total pressure 70 000 Pa, temperature 279K) with that available at sea level.

A8 At 3000 meters the amount of oxygen in one breath 3.1 x 10-3 mol. Hence at this

altitude we receive about 78% of the normal amount of oxygen in one breath.

Q9 The mean pressure in the aorta is 100 mmHg and a radius 0.9 cm. What is the wall

tension in the aorta?

A9 Laplace’s law : Tension for cylindrical membrane T = P r

The wall tension in the aorta is T={100 mmHg}{1333 (dynes/cm2 )/(mmHg)}{0.9 cm} =1.2 x

105 dynes/cm = 1200 N/m

Q10 Isolated alveoli in lungs are kept inflated to a radius of 0.15 mm by an internal pressure

4 mmHg higher than that outside the alveoli. What is the surface tension of the

surfactant-containing fluid that coat the alveoli? Assume spherical alveoli.

A10 Laplace’s law for spherical membrane is T = Pr/2.

For a fluid coated bubble there are liquid-air interface inside and outside the bubble, both

contributing surface tension. The membrane tension is then T = 2 ST, with ST=surface tension

of the fluid.

The surface tension required is ST = P r/4 = {(4)(1333)(0.015)}/4 = 20 dynes/cm

Tutorial FLUID

Density of fluid ρ = m/v Laplace’s law: T = P r for cylindrical membrane

Pressure P = F/A P = Po + ρ g h T = ½ P r for spherical membrane

Flow rate or volume flux V = A v A1 v1 = A2 v2

Bernoulli’s equation: P + ½ ρ v2 + ρ g y = constant

Poiseuille’s law:

Dalton’s law: Total pressure = the sum of individual gas pressure

Boyle’s law for ideal gas: P V = constant P V = n R T