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Gal Fluid Gallon

Fluid Mechanics Help?
Freshwater flows steadily into an open 55-gallon drum initially filled with seawater. The freshwater mixes thoroughly with the sea water and the mixture overflows out of the drum. If the freshwater flowrate is 10 gal/min, estimate the time in seconds required to decrease the difference between the density of the mixture and the density of the freshwater by 50%.
This is really not a fluid mechanics problem but rather a simple first order D.E. problem...
Q(t) = the quantity of salt in tank at time t
Q(0) = the quantity of salt in tank at time zero
The salt concentration is C = Q(t) / Volume(t)
dQ/dt is the instantaneous rate of change of the salt concentration, thus
dQ/dt = (Cin)(Flow in) - (Cout)(Flow out)
dQ/dt = (Cin)(Flow in) - (Qout(t)/Volume(t)) (Flow out)
Since freshwater has zero salt, Cin = 0 and the first term drops away
For simplicity, let's let Q equal the salt in tank solution at time t
The volume in the tank is fixed at 55 gallons and the flow in, 10 GPM, equals the flow out.
dQ/dt = - ( Q lbs / 55 gal )( 10 gal/min )
dQ/dt = -10Q / 55
Move Q to the LHS and then integrate
∫ 1/Q dQ = -10/55 ∫ dt
ln Q = -10t/55 + C
Then exponentiate
Q(t) = [ e^C ] [ e^(-10t/55) ]
At t = 0 then Q(0) = e^C
So we can say...
Q(t) = Q(0)e^(-10t/55)
Let's let Q(0) = 1 and then we need to find Q(t) = 1/2
1/2 = e^(-10t/55)
t = (-55/10)ln(1/2)
t = 3.8 minutes
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American DJ SNOW GAL - Snow Fluid - 1 Gallon | ![]() |
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US $19.99 | 26d 5h 17m |
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AMERICAN DJ SNOW GAL ONE GALLON SNOW FLUID JUICE NEW | ![]() |
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US $24.95 | 29d 9h 35m |
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American Dj Standard Fog Juice Fog Fluid Gallon Fog Machine Fluid - New | ![]() |
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US $24.99 | 29d 7h 40m |
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American DJ 1 Gallon Gal Snow Flurry Machine Fluid Juice NEW | ![]() |
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US $19.95 | 25d 9h 1m |
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AMERICAN DJ SNOW GAL ONE GALLON FLUID FOR SNOW FLURRY | ![]() |
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US $24.95 | 24d 17h 3m |
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NEW AMERICAN DJ SNOW GAL ONE GALLON SNOW FLUID JUICE | ![]() |
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US $24.95 | 14d 4h 51m |
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Pack of 4 SNOW GAL liquid fluid gallon high output bigger & denser snow B2DJ | ![]() |
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US $159.99 | 16d 1h 42m |
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Pack of 2 SNOW GAL liquid fluid gallon high output bigger & denser snow B2DJ | ![]() |
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US $79.99 | 16d 1h 40m |
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SNOW GAL liquid fluid gallon high output bigger & denser snow B2DJ | ![]() |
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US $39.99 | 16d 1h 39m |
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Martin Pro Haze Fluid - 2.5 Gallons of Premium Quality Haze | ![]() |
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US $79.99 | 24d 3h 58m |
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AMERICAN DJ SNOW GAL liquid fluid gallon high output bigger & denser snow | ![]() |
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US $39.99 | 13d 3h 10m |
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Lot of 4 AMERICAN DJ HAZE GAL gallons oil based haze generator hase hazer fluid | ![]() |
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US $199.96 | 12d 2h 33m |
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Lot of 2 AMERICAN DJ HAZE GAL gallons oil based haze generator hase hazer fluid | ![]() |
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US $99.98 | 12d 2h 31m |
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*** Gallon Gal FOG & SMOKE JUICE FLUID- for all FOGGERS | ![]() |
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US $22.95 | 9d 13h 28m |
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AQUA WATER LENS PARABOLA 100 GALLONS
Chemistry Dimensional Analysis Help!?
I need help with two problems in chemistry that need done by dimensional analysis.
First.
Which is larger a half gallon of milk (0.500 gal) or a 2 L of pop (2.00 L)?
It gives me these equations
1 quart = 32 fluid ounces (exact) 1.0576 quarts = 1000.0 cm^3 4 quarts = 1 gallon (exact)
The second problems is...
The preferred SI unit of area is square meter, land is often measured in acres. How many square kilometers is a 5.5 acre plot?
Equations...
1 acre = 160 rod^2 1 rod = 5.5 yards 40 rods = 1 furlong (exact)
8.00 furlongs = 1mile 1 meter = 1.0936 yards
If anyone could help it would be greatly appreciated!
Question 1-
1 quart = 32 fluid ounces (exact)
1.0576 quarts = 1000.0 cm^3 =mL
4 quarts = 1 gallon (exact)
1mL =1*10^-3 L
Passing 0.500 gal to quarts
0.500 gal *4 quarts/1 gal = 2 quarts
Passing to mL
2 quarts *1000.0 mL/1.0576 quarts= 1891 mL
Passing to L
1891 mL*1*10^-3 L/1mL= 1.891 L
Since 0.500 gal are 1.891 L you have less milk than pop (2.00 L)
Question 2-
1 acre = 160 rod^2
1 rod = 5.5 yards
40 rods = 1 furlong (exact)
8.00 furlongs = 1mile
1 meter = 1.0936 yards
1 m= 1*10^-3 km
Acre to rod^2
5.5 acre* 160 rod/ 1 acre= 880 rod^2
Rod^2 to rod
Square root of 880=29.66 rod
From rod to yards
29.66 rod* 5.5 yards/1 rod = 163.1 yard
From yard to meter
163.1 yard*1 meter /1.0936 yard= 149.19 meter
From meter to km
149.19 meter *1*10^-3 km /1 meter= 0.14919 km
From km to km^2
(0.14919 km )^2=0.0222 km^2

















