Calculating River Water Volume Per Minute

This problem asks us to determine the volume of water that flows from a river into the sea each minute, given the river's dimensions and flow rate. We are provided with the depth, width, and the speed at which the water flows.

Here are the given parameters:

• River Depth: 6 m
• River Width: 35 m
• Flow Rate: 2.5 km/h

To find the volume of water flowing per minute, we need to calculate the volume of a section of the river water that passes a fixed point in one minute. Imagine this section as a rectangular prism. Its dimensions would be the width of the river, the depth of the river, and the distance the water travels in one minute (which is the flow rate converted to meters per minute).

First, let's convert the flow rate from kilometers per hour (km/h) to meters per minute (m/min).

• 1 kilometer (km) = 1000 meters (m)
• 1 hour (h) = 60 minutes (min)

So, the flow rate in m/min is calculated as:

\[ \text{Flow Rate (m/min)} = \left(2.5 \text{ } \frac{\text{km}}{\text{h}}\right) \times \left(\frac{1000 \text{ m}}{1 \text{ km}}\right) \times \left(\frac{1 \text{ h}}{60 \text{ min}}\right) \]

\[ \text{Flow Rate (m/min)} = \frac{2.5 \times 1000}{60} \text{ } \frac{\text{m}}{\text{min}} \]

\[ \text{Flow Rate (m/min)} = \frac{2500}{60} \text{ } \frac{\text{m}}{\text{min}} \]

\[ \text{Flow Rate (m/min)} = \frac{250}{6} \text{ } \frac{\text{m}}{\text{min}} = \frac{125}{3} \text{ } \frac{\text{m}}{\text{min}} \]

Now that we have the flow rate in meters per minute, we can calculate the volume of water flowing into the sea per minute. The volume is the product of the river's width, depth, and the distance the water travels in one minute (flow rate in m/min).

\[ \text{Volume per minute} = \text{Width} \times \text{Depth} \times \text{Flow Rate (m/min)} \]

\[ \text{Volume per minute} = 35 \text{ m} \times 6 \text{ m} \times \frac{125}{3} \text{ } \frac{\text{m}}{\text{min}} \]

Let's perform the multiplication:

\[ \text{Volume per minute} = (35 \times 6 \times \frac{125}{3}) \text{ } \text{m}^3/\text{min} \]

We can simplify the calculation by dividing 6 by 3:

\[ \text{Volume per minute} = (35 \times 2 \times 125) \text{ } \text{m}^3/\text{min} \]

\[ \text{Volume per minute} = (70 \times 125) \text{ } \text{m}^3/\text{min} \]

Now, let's calculate $70 \times 125$:

\[ 70 \times 125 = 70 \times (100 + 25) = (70 \times 100) + (70 \times 25) = 7000 + 1750 = 8750 \]

So, the volume of water that runs into the sea per minute is $8750 \text{ m}^3$.

Comparing this result with the given options:

Our calculated volume matches Option 4.

Revision Table: Key Concepts

Additional Information: Understanding River Flow

The flow of a river is a complex phenomenon, but for simplified calculations like this, we treat the river channel as having a uniform rectangular cross-section. The flow rate represents the average speed of the water. The volume flow rate is a crucial concept in hydrology and environmental science, helping us understand water resources, flood dynamics, and the transport of substances within rivers. The unit m³/min (cubic meters per minute) is a standard unit for expressing volume flow rate.

In this specific problem, we calculated the volume of water that flows past a point (like the river mouth entering the sea) every minute. This volume is essentially the volume of a slug of water whose length is the distance the water travels in one minute, and whose cross-sectional area is the area of the river channel ($35 \text{ m} \times 6 \text{ m}$).