How do I find how long it takes to drain one half of the initial volume of the conical tank . and what fraction of the full drain time is it?
To find how long it takes to drain one half of the initial volume of the conical tank, you need to know the volume of the tank and the rate at which it drains. Let's assume that the initial volume of the conical tank is V and the drainage rate is R.
The time it takes to drain one half of the initial volume can be calculated using the formula:
Time = (0.5 * V) / R
This formula takes the initial volume of the tank (V), multiplies it by 0.5 to find one half, and then divides it by the rate of drainage (R) to get the time it takes to drain half of the volume.
To determine the fraction of the full drain time, you need to compare the time it takes to drain one half of the initial volume with the time it takes to drain the full volume. Let's denote the full drain time as T.
The fraction of the full drain time that it takes to drain one half of the initial volume can be calculated using the formula:
Fraction = (0.5 * V) / (V / R)
Simplifying this equation, we have:
Fraction = (0.5 * V) * (R / V)
The volume of the tank (V) cancels out, leaving you with:
Fraction = 0.5 * R
This means that the fraction of the full drain time that it takes to drain one half of the initial volume is half of the drainage rate (R).
In summary, to find how long it takes to drain one half of the initial volume of a conical tank, use the formula (0.5 * V) / R, and to find the fraction of the full drain time, use the formula 0.5 * R.