CHAPTER 9 FLUID DYNAMICS BOARD PROBLEMS
1. The rate of flow of water through a horizontal pipe is 2.4 m3/min. Determine the velocity of flow at a point where the diameter of the water pipe is A) 16 centimeters and B) 6 centimeters.
CHAPTER 9 FLUID DYNAMICS BOARD PROBLEMS
2. Water squirts from a syringe at a speed of 45 m/s. The diameter of the needle opening is 0.012 cm. Determine the pressure difference between the water inside the syringe and the air outside. Assume the syringe is horizontal and also that the flow speed inside the syringe is zero.
CHAPTER 9 FLUID DYNAMICS BOARD PROBLEMS
3. The water supply of a building is fed through a main 4-centimeter diameter pipe. A 1.5 centimeter diameter faucet tap located 3 meters above the main pipe is observed to fill a 25-liter container in 45 seconds. A) What is the speed at which the water leaves the faucet? B) What is the gauge pressure (atmospheric pressure sealed out) in the 6-centimeter pipe?
CHAPTER 9 FLUID DYNAMICS BOARD PROBLEMS
A PHYSICAL PRESENTATION OF THE COHESION-TENSION THEORY BY THE USE OF FLUID DYNAMICS Most of the water gathered by the roots of a plant is eventually lost to the air as water vapor. The water lost to the environment, through transpiration is greater than the water gathered by the plant at the root system. This difference in the rate at which water is gathered and lost is the focus of this term paper. I will attempt to show a pressure difference between the top and bottom of the plant, by using the equation of continuity and the Bernoulli equation. A pressure difference for the ash tree will be calculated along with a general solution. The ash tree will be used only as an example to show this pressure difference. One must not over generalize from this example due to the inherent differences in plants. The solution is an example to be followed by other teachers with the idea that they use their data for calculations. The following measurements must be taken in order to make the calculation. 1. Diameter of transport vessel. 2. Height of the plant. 3. Volume of water transpired by the plant. 4. Time of this transpiration.
5. Volume of water absorbed by the plant. (Only for a more accurate and rigorous calculation) Data for the ash tree include: 1. Transport vessel diameter = 65m. = 65 X 10-6 meters 2. Height of ash tree = 20 meters. 3. Volume of water transpired = 34 grams 4. Volume of water gathered = 12 grams 4. Time of transpiration = 2 hours Find the velocity of the water by using the volume and time of transpiration given in graph. Volume flow rate at the top of tree Volume flow rate at bottom of tree
3 3 3 3_ _
3_
24 1 1 12 1 1.003 .0016
2 1 3600sec 2 1 3600sec
Converting centimeters to meters Converting centimeters to meters
.003
grams cm hour cm grams cm hour cm
hours gram s hours gram s
cm
s
3 3 3 3 3_ _ _9 9
6 3 6 3
1 13.3 10 .0016 1.6 10
1.0 10 1.0 10
m m cm m m
cm s s cm s
2
26 6 2 9 2
Determine the area of the vessel
2
32.5 10 1.05625 10 3.32 10
A r radius diameter
A m A m A m
CHAPTER 9 FLUID DYNAMICS BOARD PROBLEMS
Use the equation of continuity to find the velocity of the transpiring water at the top of the tree and also the velocity of the water absorbed by the roots.
_9 3
9 2
_9 3
9 2
, ,
3.3 101.004
3.32 10
3.6 10.5020
3.32 10
Top
Top
Q Av Where Q flow rate A area v velocity
Q m mv v v
A sm s
Q m mv v v
A sm s
3
2 21 12 2
2 21 12 2
10001.
0
&
In order for us to make this calculation wemust make an assumption
kgThe water must be assumed to be pure thus making
m
P gh V P gh V
Since h
P V P gh V
Collecting pressures on a side taking V to o
2 21 12 2
2 21 12 2
2 2
3 2
2 2 2
3 2 2 2
3
( )
1000 9.8 20 .5 1.004 .5 .5020
1000 196 .504 .126
1000 196
ther side
P P gh V V
Factoring
P gh V V
kg m m mP m
m s s s
kg m m mP
m s s s
kgP
m
2
2
23
3 2 3 2
3
.378
196.378 10
196.378 10
m
s
kgm Nm NP
m s m m
P Pa
