Estimate Olympic swimming pool problem using Order of Magnitude Calculation:
An Olympic swimming pool is roughly 45 m long and 33 m wide.
How long will it take to fill such a pool with an ordinary garden hose?
you need to specify
(a) the depth of the pool
(b) the flow rate of an "ordinary garden hose"
To estimate how long it will take to fill an Olympic swimming pool using an ordinary garden hose, we can employ an order of magnitude calculation.
Step 1: Calculate the volume of the pool
The volume of a rectangular pool is determined by multiplying its length, width, and depth. Since the depth of the pool is not provided, we will assume a typical depth of around 2 meters for an Olympic swimming pool.
Volume = length × width × depth
Volume = 45 m × 33 m × 2 m
Volume ≈ 2970 m³
Step 2: Determine the flow rate of the garden hose
An ordinary garden hose typically has a flow rate of around 10 liters per minute. To convert this to a more relevant unit, we'll multiply by 60 to get liters per hour.
Flow rate = 10 L/min × 60 min/hr
Flow rate = 600 L/hr
Step 3: Calculate the time to fill the pool
To figure out how long it will take to fill the pool, divide the volume of the pool by the flow rate of the garden hose.
Time = Volume / Flow rate
Time = 2970 m³ / 600 L/hr
Before performing the division, we need to convert the volume units from cubic meters to liters.
1 m³ = 1000 L
Time = (2970 m³ × 1000 L/m³) / 600 L/hr
Time ≈ 4950 hr
So, it will take approximately 4950 hours to fill the Olympic swimming pool using an ordinary garden hose.