Let's go snow rally!
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For people who don't care for explanations and always want to just cut straight to the answer... 0.294! There, now you didn't have to read it. But all you engineers out there might want to read it and flame away!
Sorry it's been a couple of days since I checked the thread. I just got busy with stuff, so let's see if we can make sense of this. Hopefully you have figured it out by now, but if not, this explanation comes with zero guarantee! But it might get you thinking along the right lines. Also bear in mind that I don't have my fluids book with me right now either...
I think the crux of the problem is that the 15 constrictions are in series. That means that there is going to be a loss every two inches along the pipe. There will also be a small head loss between each constriction due to the boundary layer of the fluid along the inside of the wall of the pipe, but I think that loss will be negligible when compared to the losses occurring at the constrictions. So each constriction will be a key point along the pipe to consider.
However, solving the flow parameters every two inches along the pipe could get real tedious real fast, so we make one assumption that I think is true: The constriction geometries and associated efficiencies are identical! So how do we consider them all in one fell swoop? We know that from your text, the total pressure on the down-stream side of the orifice will be 62% of that on the up-stream side. Then, at the next orifice, we have a similar efficiency, and so on. The total efficiency of the pipe is therefore 0.62x0.62x0.62... or more concisely, 0.62^15. This gives a total efficiency of 0.000769.
We will make another assumption at this point, and check it later. We will assume that the 40 psi you list is the total pressure, or stagnation pressure. As there is a total pressure loss across the pipe, the total pressure at the opposite end will be 40psi x 0.000769 = 0.0308 psi. For simplicity, we can convert that to lb/ft^2. It is 0.0308 psi x 144 = 4.43 psf.
Now we can assume the four key assumptions of Bernoulli's solution (inviscid, incompressible, isentropic, and irrotational) shown below:
Po = P + 0.5 rho V^2 + gz
As the flow in this particular problem lies perpendicular to the ambient gravitational field (i.e. horizontal), the gz term is zero and will be ignored for this analysis. We know Po = 4.43 psf, and that the density of water is roughly 1.9403 slug/ft^3. Another assumption is that the 40 psi that you originally provided was a gage pressure, meaning that it was the total pressure minus the static pressure of the air at the outlet of the pipe. Therefore the static pressure (P) also drops out of the equation if we study the flow at the exit of the pipe. At this point the astute observer will realize that the only unknown variable left in the equation is the velocity of the water at the exit of the pipe! Some quick algebra brings us to the following equation:
V = sqrt(2*Po/rho)
I get a velocity of 2.14 ft/s at the end of the pipe. We also know the area of the pipe outlet, as you kindly provided the diameter and geometry of the exit.
A = pi/4*d^2 = pi/4*(3/4 in)^2 = 0.442 in^2 = 0.00307 ft^2
Volumetric flow rate can be calculated by multiplying the exit velocity and the exit area together, and results in a flow rate of 0.00656 ft^3/sec. Converted to gallons per minute, it comes out to about 0.294 gal/min.
Don't know how realistic that actually is, but I hope it is of some use to you! Fluid flow is definitely interesting stuff!
Alpine II 318isComment
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Finnaly bought a truck. 2002 Tacoma, ext cab, 72k miles, 5 speed, trd, for $13k. Only catch is now I have to go to California to get it. I figured my last 3 cars have come from there - the E36 M3, M roadster, and the E39 wagon, so why break the trend?Comment
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Not bad, and yeah, California is a decent place to buy cars.
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Been looking here for a while, and all the ones around here beat with 150k on them. Seems like they are all the same price regardless of miles, so might as well get one with low miles. Now to plan a road trip.Comment
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Where in California is it?Comment
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San Diego. So far the plan is up the coast to Santa cruz, ride mountain bikes, then over to Tahoe, ski, long haul across the desert and stop in telluride to ski and ouray to ice climb, and then back to golden. Followed a week later it's going up to Banff alberta and onto the Yukon. So much for being low miles!Comment
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Fawk me....Deal just fell through. Long story short, seller tells me he's selling for his girlfriend, who is the original owner. I check carfax, and it lines up, 1 owner, mileage lines up, no accidents, only odd thing is its listed as registered in San fran, and car is for sale in San diego. He tells me they just moved down there. Seems resonable enough. We work out a deal, I book tickets (me and the GF), and call him back with the details of when to meet me etc. I ask for his email so I can send him the info, and he says he doesn't have one. Who the F doesn't have an email?? I'm not buying a Delorean here, its 2011, WTF is your email? At this point, I double check that she's going to be there to sign over the title since its in her name. He says, that she's not going to be there. So I suggest he get a copy of her licence and a notorized letter authorizing him to sell. He says that might be tricky, he'll look into it and call me back. At this point my spider senses are tingling, and the red flags are up. I google his phone number and he's selling a bunch of vehicles, including wrecked toyotas. He calls back and says she's out of town and he's not going to be able to get a copy of her license or anything, and says its not like its stolen or anything. OK, enough BS, I tell him he's full of shit and deal is off. Not sure what the real story is, but I'm not flying to California to get screwed. Cancelled flights (suprisingly no fees!), and the search for a clean tacoma continues!
So maybe that wasn't the short version.....
Maybe its a sign I should stick to BMWs.Comment
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Well at least you got it sorted out BEFORE you got to California. Good luck with the search.
- E30, DSM, Golf R, Mazda 3 Skyactiv
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Dude Find another one in San Diego and we can caravan back when I bring the TR6 home - meaning when I break down after 20 miles you can tow me home.JOY IS AN E30...
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were you buying from vlad's cousin?Comment
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