Question

SLADER A bottle with a volume of 199 U. S. fluid gallons is filled at the rate of 1.6 g/min. (Water has a density of 1000 kg/m3, and 1 U.S. fluid gallon = 231 in.3.) How long does the filling take?

Answer 1

Answer:

$\Delta t = 124.375\,min$

Step-by-step explanation:

Given that volumetric rate is constant in time, the time needed to fill the bottle is:

$\Delta t = \frac{V_{bottle}}{f}$

$\Delta t = \frac{199\,gal}{1.6\,\frac{gal}{min} }$

$\Delta t = 124.375\,min$

Answer 2

The filling takes 326.9 days

To solve this question, we must first convert the volume of the 199 U.S fluid gallons to cubic meters and find the mass of fluid.

What is Volume?

The volume of an object is defined as the dimensional space enclosed in a closed region.

From the information given:

• The filling of the bottle = 1 U.S fluid gallon = 3.785 L

199 U.S fluid gallon will be:

= (199 × 3.785 )L

= 753.215 L

However converting the volume in Liters to cubic meters, we know that:

• 1000 L = 1 cubic meter

Hence;

• 753.215 L = 0.753215 m³

Using the relation:

$\mathbf{density = \dfrac{mass}{volume}}$

mass = density × volume

mass = 1000 kg/m³ × 0.753215 m³

mass = 753.215 kg

From the parameters given:

• the rate at which the gallon is filled = 1.6 g/min

Using the relation for time:

TIme(t) = mass/rate

Time (t) = 753.215 kg/1.6 g/min

TIme (t) = (753.215  × 1000)g / 1.6 g/min

Time (t) = 470759.375 min

TIme (t) = 326.9 days

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