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Gal Fluid Gallon
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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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

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