It has been a while since I droned out some back of the envelope calculations, I'm sure my devoted readers - I hesitate to call them fans - are in need of a fix.
It all started with a stroll...
Twas a sedate day today. I strolled in to college to do some experiments for the forthcoming conference. On my way, I chanced upon a chap hosing-down a tall petrol station sign. Initially, I was rather concerned because the water was sprinkling onto the foot path and I was not prepared to contend in a wet t-shirt contest.
As I worried over this, a woman approached the "splash zone." The chap was the considerate sort and pointed the hose stream onto the Station's courtyard. I started thinking about calculating the water pressure and velocity, given the angle, initial elevation and distance travelled by the jet.
I expected it to be somewhat tricky to do in my head. As luck would have it, I noticed the man was spraying almost to vertical. I eyeballed a stagnation height for the stream and used the Bernoulli equation to get the initial velocity as ui = [2gh]1/2).a Since my calculation skill(z) are poor, I took some shortcuts and got 10.9 m/s (h = 6 m, g = 9.81 m/s2 actually gives 10.85 m/s). Hand-in-hand with this was the pressure of the water coming out of the hose, ~0.6 bar (gauge).b
Once I had a value for the pressure, I was rather disappointed in the pressure head, since I was expecting over a 1 bar (gauge). The Dublin City Council state they "aim to maintain a pressure of at least 12m [slightly less than 1.2 bar (gauge)] in the water-main network at anytime of the day. It will fluctuate as a result of varying demand." The water was coming from a connection to the water mains, it was a dodgy connection ("Cowboys Ted!") with water gushing out of its sides. If it was the same as the water arriving in the hose then every thing finishes up nicely. Otherwise DCC let me down in this instance. :'(
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My musings occupied me until I reached the UCD campus.
Therein, I found myself admiring the manifold greens of the landscape. Since hydrostatics had been on my mind, I was impressed that the trees can draw water up to their topmost branches without any drama- they feckers just stand there! I had some trouble remembering what physical actions they were exploiting to get this done. Osmosis and osmotic pressure stuck in my head. Boy-howdie! that was only half the story! [I understand that enthusiasm can be infectious... for my sake lets hope so]
Osmosis gets the ball rolling in the tree roots. It is the diffusion of molecules across a permeable membrane, specifically a solvent is transferred from a solvent rich side to a solvent poor sidee [or whatever satisfies the Gibbs equation (ΔG=ΔH-TΔS)f for the system].
The water in the soil passes through the permeable roots cells and is then drawn up the xylem to the leaves. The water is pushed and pulled up the tree. The pressure induced by increased water content in the roots serves to push it upwards.
Since the xylem are thin tubes, the viscous forces and surface tension make the water streams difficult to break. Water evaporates from the leaves, which serves to draw the water upwards, and the capillary action prevents the streams from being broken [- more or less].g
Well, I don't know about you guys, but I certainly learned something today - even when i get out more, I need to get out more.
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a I neglected the effect air has on the water stream, I thought it reasonable since air has a density of about 1/1000 and would do little to reduce the momentum of the stream.c
b I can only comment on the velocity and pressure on the atmospheric side of the system because I did not know how much energy is lost due to friction in the pipe, joints, elbows and going through the orifice.d
c I confidently confirm this is an acceptable assumption
d Yes. It sounds disgusting... while on the topic of disgusting sounding engineering terms, a piece used to join sections of piping is known as a flange. Not a topic that can be broached with a straight face by undergraduate and childish engineers
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e Similar processes happen in your kidneys [both real and artificial ones], it is how salt water fish die in fresh water and it can be crystallization technique.
f I was first exposed to that innocuous equation when I was preparing for the International Chemistry Olympiad in 2002 while in DCU. It has 4 variables and 1 multiplication. Simple.
Nevertheless, I had tremendous difficulty remembering it then.
Luckily I got a second run at it in College in first year Chemistry and Engineering thermodynamics. By the time it came at me in second year Thermodynamics, I had a handle on it. It is a useful principle. If ΔG <0>g The link I gave for osmosis, unfortunately bland-looking basic text, goes through the pitfalls of some asssumptions laid out above, out of lazi- ugh... I mean - as a test I have given a crude description of the mechanisms involved. I hope to encourage "you kids" to read up and show me how "cool" you are by knowing more than I do about this stuff.
It all started with a stroll...
Twas a sedate day today. I strolled in to college to do some experiments for the forthcoming conference. On my way, I chanced upon a chap hosing-down a tall petrol station sign. Initially, I was rather concerned because the water was sprinkling onto the foot path and I was not prepared to contend in a wet t-shirt contest.
As I worried over this, a woman approached the "splash zone." The chap was the considerate sort and pointed the hose stream onto the Station's courtyard. I started thinking about calculating the water pressure and velocity, given the angle, initial elevation and distance travelled by the jet.
I expected it to be somewhat tricky to do in my head. As luck would have it, I noticed the man was spraying almost to vertical. I eyeballed a stagnation height for the stream and used the Bernoulli equation to get the initial velocity as ui = [2gh]1/2).a Since my calculation skill(z) are poor, I took some shortcuts and got 10.9 m/s (h = 6 m, g = 9.81 m/s2 actually gives 10.85 m/s). Hand-in-hand with this was the pressure of the water coming out of the hose, ~0.6 bar (gauge).b
Once I had a value for the pressure, I was rather disappointed in the pressure head, since I was expecting over a 1 bar (gauge). The Dublin City Council state they "aim to maintain a pressure of at least 12m [slightly less than 1.2 bar (gauge)] in the water-main network at anytime of the day. It will fluctuate as a result of varying demand." The water was coming from a connection to the water mains, it was a dodgy connection ("Cowboys Ted!") with water gushing out of its sides. If it was the same as the water arriving in the hose then every thing finishes up nicely. Otherwise DCC let me down in this instance. :'(
__________________________________________________________________
My musings occupied me until I reached the UCD campus.
Therein, I found myself admiring the manifold greens of the landscape. Since hydrostatics had been on my mind, I was impressed that the trees can draw water up to their topmost branches without any drama- they feckers just stand there! I had some trouble remembering what physical actions they were exploiting to get this done. Osmosis and osmotic pressure stuck in my head. Boy-howdie! that was only half the story! [I understand that enthusiasm can be infectious... for my sake lets hope so]
Osmosis gets the ball rolling in the tree roots. It is the diffusion of molecules across a permeable membrane, specifically a solvent is transferred from a solvent rich side to a solvent poor sidee [or whatever satisfies the Gibbs equation (ΔG=ΔH-TΔS)f for the system].
The water in the soil passes through the permeable roots cells and is then drawn up the xylem to the leaves. The water is pushed and pulled up the tree. The pressure induced by increased water content in the roots serves to push it upwards.
Since the xylem are thin tubes, the viscous forces and surface tension make the water streams difficult to break. Water evaporates from the leaves, which serves to draw the water upwards, and the capillary action prevents the streams from being broken [- more or less].g
Well, I don't know about you guys, but I certainly learned something today - even when i get out more, I need to get out more.
__________________________________________________________________
__________________________________________________________________
a I neglected the effect air has on the water stream, I thought it reasonable since air has a density of about 1/1000 and would do little to reduce the momentum of the stream.c
b I can only comment on the velocity and pressure on the atmospheric side of the system because I did not know how much energy is lost due to friction in the pipe, joints, elbows and going through the orifice.d
c I confidently confirm this is an acceptable assumption
d Yes. It sounds disgusting... while on the topic of disgusting sounding engineering terms, a piece used to join sections of piping is known as a flange. Not a topic that can be broached with a straight face by undergraduate and childish engineers
__________________________________________________________________
e Similar processes happen in your kidneys [both real and artificial ones], it is how salt water fish die in fresh water and it can be crystallization technique.
f I was first exposed to that innocuous equation when I was preparing for the International Chemistry Olympiad in 2002 while in DCU. It has 4 variables and 1 multiplication. Simple.
Nevertheless, I had tremendous difficulty remembering it then.
Luckily I got a second run at it in College in first year Chemistry and Engineering thermodynamics. By the time it came at me in second year Thermodynamics, I had a handle on it. It is a useful principle. If ΔG <0>g The link I gave for osmosis, unfortunately bland-looking basic text, goes through the pitfalls of some asssumptions laid out above, out of lazi- ugh... I mean - as a test I have given a crude description of the mechanisms involved. I hope to encourage "you kids" to read up and show me how "cool" you are by knowing more than I do about this stuff.
Sad to say that "flange" has lost a lot of its churlishness ... I'm getting old.
ReplyDeleteAnonymous Tony