Natural Gas Consumption Calculation in Cubic Feet and Seconds

[Mivz18]

Problem: The consumption of natural gas by a company satisfies the empirical equation V=1.50t + 0.800 00(t squared), where V is the volume in millions of cubic feet and t the time in months. Express this equation in units of cubic feet and seconds. Assign proper units to the coefficients. Assume a month is equal to 30.0 days.

My work:

From the equation given, I took each part of the right and converted the months variable to seconds.

1.50(t months) * (t 30 days) * (t 24 hours) * (t 60 min) * (t 60 sec.)
-------------- ---------- ---------- --------- ----------
1 (t month) (t 1 day) (t 1 hr.) (t 1 min)


= 3.888E6(t sec.)

Then I repeated the conversion multiplication fractions with 0.008 00 and squaring the other numbers and reaching a value of 5.37477E9(t sec)^2

My new equation is then V= 3.888E6(t sec.) + 5.37477E9(t sec.)^2

dividing by a million to convert millions of cubic feet to cubic feet, I get:

V=3.889E6(t sec.) + 53747.7(t sec.)^2

However, the book gives an answer of 0.579t (ft cubed/sec.) + 1.19E-9t^2 (ft cubed/sec. squared)
Is not assigning units to the coefficients screwing me up or is there another problem with my calculations?

 

[learningphysics]

Problem: The consumption of natural gas by a company satisfies the empirical equation V=1.50t + 0.800 00(t squared), where V is the volume in millions of cubic feet and t the time in months. Express this equation in units of cubic feet and seconds. Assign proper units to the coefficients. Assume a month is equal to 30.0 days.

My work:

From the equation given, I took each part of the right and converted the months variable to seconds.

1.50(t months) * (t 30 days) * (t 24 hours) * (t 60 min) * (t 60 sec.)
-------------- ---------- ---------- --------- ----------
1 (t month) (t 1 day) (t 1 hr.) (t 1 min)


= 3.888E6(t sec.)

Remember that the given formula requires t (the time in months). When dealing with t you have to be careful... I'd do it like this:

let a=time in seconds.

a = t months * (30days/1 month) * (24 hours/1day)*(60min/1hr)*(60s/1min)
so a= 2.592E6 * t seconds

So now solve for t, and then plug back into the original equation.

So t=a/2.592E6 . Plug a/2.592E6 into the original equation. Think of it like this. You've got the time in seconds a, then getting the time in months t, in terms of a...

So you'll then get an equation in terms of a, where a is in seconds. Volume is still in millions of cubic feet.

dividing by a million to convert millions of cubic feet to cubic feet, I get:

To get from millions of cubic feet to cubic feet, you need to multiply by a million, not divide.

 

[wais]

Your calculations seem to be correct, however, you did not assign units to the coefficients in your final equation. This can lead to confusion and difficulty in understanding the units of the equation. The units of the first coefficient should be (ft^3/sec) and the units of the second coefficient should be (ft^3/sec^2). It is important to always include units in your calculations to avoid any confusion or errors.