Calculating Average Water Flow Rate with f(t) Function

In summary, the rate at which water is sprayed is given by the function f(t). To find the average rate of water flow during the time interval 0<t<4, we can use the formula ∫f(t)/4 evaluated from 0 to 4. This is because f(t) represents the rate of water and ∫f(t) represents the total water. Therefore, the average rate of water flow is equal to the total water divided by the time interval.
  • #1
fiziksfun
78
0
the rate at which water is sprayed is given by the function f(t)

during the time interval 0<t<4, what is the average rate of water flow??

I'm confused whether to use the formula

f(4)-f(0) / (4-0)

OR

[tex]\frac{1}{4}[/tex][tex]\int[/tex]f(t) evaluated from 0 to 4.

help!
 
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  • #2
Hi fiziksfun ! :smile:

Hint: Suppose f(t) is a constant, C. Then f(4) = f(0) = C.

So which formula is right? :smile:
 
  • #3
i'm kind of slow, so i still don't understand :[
can you help me more??
 
  • #4
Sure! :smile:

If f(t) = C, a constant, then obviously the average of f(t) is C.

But f(4)-f(0) / (4-0) = (C - C)/4 = 0, which obviously is wrong. :frown:

And ∫f(t)/4 = ∫C/4 (evaluated from t = 0 to 4) = C, which equally obviously is right! :smile:

This works for any f(t), because f(t) is the rate of water, so ∫f(t) is the total water.

And so the average rate of water = total/time = ∫f(t)/4. :smile:
 
  • #5
ah, i think i understand, thank you!
 

1. What is a f(t) function?

A f(t) function represents the rate at which water is flowing at a specific time, t. It is a mathematical function that takes into account various factors such as volume, pressure, and time.

2. How do you calculate average water flow rate using a f(t) function?

To calculate the average water flow rate, you need to integrate the f(t) function over a specific time period and then divide it by the total time. This will give you the average flow rate over that time period.

3. What units are used for average water flow rate?

The units for average water flow rate can vary depending on the system of measurement being used. In the metric system, the most commonly used unit is liters per second (L/s), while in the US customary system, gallons per minute (GPM) is often used.

4. Can the f(t) function be used to calculate average water flow rate for any type of system?

Yes, the f(t) function can be used to calculate average water flow rate for any type of system as long as the necessary variables are included in the function.

5. How accurate is the average water flow rate calculated using a f(t) function?

The accuracy of the average water flow rate calculation using a f(t) function depends on the accuracy of the input data and the complexity of the function. The more accurate the data and the function, the more accurate the calculated flow rate will be.

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