Question

The gas tank of a car is filled with a nozzle that discharges gasoline at a constant flow rate. Based on unit considerations of quantities, obtain a relation for the filling time in terms of the volume \(V\) of the \(\operatorname{tank}(\text { in } \mathrm{L})\) and the discharge rate of gasoline \(V(\text { in } \mathrm{L} / \mathrm{s})\)

Short answer

Short Answer: T = V / V'

Step-by-step solution

Identify the given quantities and their units

In this problem, we are given the following quantities and units: - Volume of the tank (V) given in Liters (L) - Discharge rate of gasoline (V') given in Liters per second (L/s)

Write down the equation to find the filling time

The filling time (T) can be found by dividing the volume of the tank (V) by the discharge rate of gasoline (V'). Or in other words, we can say: T (in seconds) = V (in Liters) / V' (in Liters per second)

Solve the equation for the filling time (T)

By using the equation from Step 2, we can rearrange it to find the filling time (T) in terms of the volume of the tank (V) and the discharge rate of gasoline (V'): T = V / V' This equation shows that the filling time (T) is directly proportional to the volume of the tank (V) and inversely proportional to the discharge rate of gasoline (V').