Final answer:
The average speed of the Waikato River at Huka Falls is calculated using the formula Q = v1 × w × d, where Q is the flow rate, v1 is the velocity, w is the width, and d is the depth. After converting the flow rate to cubic meters and using the given dimensions of the river at the gorge, the calculated average speed is 0.75 m/s, which does not match the provided options.
Step-by-step explanation:
The Huka Falls on the Waikato River is a significant natural tourist attraction in New Zealand, with the river flowing at a substantial average rate. To determine the average speed of the Waikato River in the gorge, we use the continuity equation for fluid flow, which states that the flow rate (volume per time) must be constant. Given an average flow rate of 300,000 liters per second, and considering the gorge narrows to 20 meters wide and 20 meters deep, we can find the average speed of the river at that point.
To calculate the speed at the gorge (v1), we use the flow rate (Q), width (w), and depth (d) of the river:
Q = v1 × w × d
First, we convert the flow rate from liters to cubic meters:
300,000 L/s × (1 m³/1000 L) = 300 m³/s
Now, using the measurements for the gorge:
300 m³/s = v1 × 20 m × 20 m
Thus, v1 = 300 m³/s / (20 m × 20 m) = 300 m³/s / 400 m² = 0.75 m/s
Therefore, the average speed of the river in the gorge is not the provided options (15 m/s, 20 m/s, 25 m/s, 30 m/s), but rather 0.75 m/s.