Al Azhar university Lama El Banna general physic

1. General Physics for Medical Sciences
Homework 5 Solution
Instructor: Dr. Hassan Ashour
Due Date: Dec 30, 2009
Solve the following questions
Q1: A 2.00 cm diameter hose carries water at 1.06 m/s. With what speed does the water exit
a 1.00 cm diameter nozzle?
Solution
= ⇒ = = =
1.06
×
(1 × 10 )
(0.5 × 10 )
= 4.24 /
Q2: By what factor will your garden watering time be cut if you switch from a 3/8 inch
diameter hose to a 5/8 inch hose? Assume nothing else is changed.
Solution: we know that the flow rate is the following
=
8
∆
Thus,
=
8
∆
=
8
∆
Thus, the ratio is
=
8
∆
8
∆
Since all the parameters are kept the same but the hose diameter, all terms drops out except
the radii
= =
5/8
3/8
= 7.716

2. The flow rate has increased by a factor of 7.716, thus the time will be reduced by the same
factor, that is
=
7.716
This gives a reduction in time equals,
× 100 = .
× 100 = 87.04%
reduction in time
Q3: A patient is to be given a blood transfusion. If the inside diameter of the 4.0 cm long
needle is 0.40 mm, the blood pressure in the arm is 2400 Pa, and the required flow is 4.0
cm³/min, how high h should the bottle be placed? (ρ = 1050 kg/m³, η =0.0040 Pa·s)
Solution
Use Poiseuille’s equation to calculate the excess pressure beyond 2400 Pa that is required to
overcome the viscosity of the blood, and then use equation = ℎ to find ℎ needed to
provide such a pressure.
=
8
∆
⇒ ∆ =
8
⇒ − =
8
⇒
= + and = ℎ
Equate both equations gives
ℎ = +
8
ℎ =
1
+
8
now, substitute your factors
ℎ =
1
1050 / × 9.8 /
2400 / +
8
4 × 10
60 × 0.04 × 0.004 .
(2 × 10 )
ℎ = 1.44

3. Q4: A jet pilot pulls his plane out of dive in such a way that his upward acceleration is 3 g’s.
What you predict as the blood pressure in the brain?
Solution
In our case, we have an upward acceleration, ( + )
With = 3
Thus, according to equation 5.16 on page 116,
= + ( + )( − )
We have, in the textbook, = 13.3 , ( + ) = 4 ≅ 40 / and
ρ = 1060 /
On the average, the height difference between brain-heart is about 0.3 , that is
( − ) = 0.3
= 13.3 × 10 +
1060 40
(−0.3 ) = 580 .
Don’t be confuse with minus sign, the brain is higher than the heart
Q5: The aorta in humans has a diameter of about 2 cm and at certain times, the blood speed
through it is about 5.5 / . What is the type of flow? Find also the flow resistance over
30 cm long segment and the power for dissipating the blood through this segment
Solution
=
2 ̅
=
2 × 1060 × 0.055 × 10
2.08 × 10−3
.
= 560.58
< 2000, ℎ ℎ
ℛ =
8
=
8 × 2.08 × 10−3
. × 0.30
(10 )
= 159 . /
= = ( ) = 159 . 3
× ( . ) × ( . / )
= .

4. Q6: The radius of an artery is increased by a factor of 1.5 (a) the pressure drop remains the
same, what happens to the flow rate? (b) If the flow rate stays the same, what happens to the
pressure drop? (Assume laminar flow).
Solution
a.
=
8
∆
And
=
8
∆
Thus,
=
8
∆
8
∆
= = =
1.5
= 5.0625
b.
=
8
∆
Thus,
∆ =
8
∆ =
8
Divide,
∆ 2
∆ 1
=
8 2
2
4
8 1
1
4
=
1
2
=
1
1.5 1
= 0.1975 ≅ 0.2