Question

If groundwater in an aquifer flows at a rate of \(0.4 \mathrm{~m} /\) day, how long does it take groundwater to move \(24 \mathrm{~m}\) ?

Short answer

It takes 60 days.

Step-by-step solution

Identify Given Information

We are given the flow rate of groundwater in the aquifer, which is \(0.4\) meters per day. We need to find out how long it takes for the groundwater to move \(24\) meters.

Set Up the Formula

To find the time it takes for something moving at a constant speed to cover a certain distance, we use the formula \( \text{time} = \frac{\text{distance}}{\text{rate}} \).

Plug in Known Values

Substitute the given values into the formula: \( \text{time} = \frac{24 \text{ m}}{0.4 \text{ m/day}} \).

Calculate the Time

Perform the division: \( \text{time} = \frac{24}{0.4} \). This simplifies to \( \text{time} = 60 \) days.

Verify Solution

Check the calculation by reasoning: if water moves \(0.4\) meters each day, then over \(60\) days, it covers \(60 \times 0.4 = 24\) meters. The calculations are consistent with the problem statement.

Key concepts

Aquifer

Aquifers are underground layers of water-bearing permeable rock or materials like gravel, sand, or silt. Water, known as groundwater, can move freely within these materials, allowing it to be stored and transmitted throughout the aquifer. Aquifers play a crucial role in providing fresh water to wells, springs, and surface water bodies.
Key characteristics of an aquifer include:

• Porosity: This is the measure of how much open space is present between the grains or within the fractures of the rock formation. A higher porosity indicates more potential storage for water.
• Permeability: This refers to the ability of the aquifer material to transmit water. Materials with high permeability, like gravel, allow water to flow more easily compared to clay, which has low permeability.

Aquifers can be classified into two main types:

• Confined Aquifers: These are bounded above and below by less permeable materials or rock layers. Water pressure can build up, allowing it to rise in wells without pumping.
• Unconfined Aquifers: These are where the water is directly recharged by rainfall or surface water as it penetrates through the ground. These are more susceptible to pollution since the water is closer to the surface.

Understanding how aquifers work helps in sustainable water management, as it ensures that groundwater resources are utilized without being depleted.

Groundwater Movement

Groundwater movement within an aquifer occurs due to gravity and pressure differences. Typically, water travels from areas of high pressure to low pressure, moving through the porous materials of the aquifer. The ability of groundwater to move is impacted by the permeability of the aquifer material.
Groundwater flow is often slow compared to surface water, with speed dependent on several factors:

• Hydraulic Gradient: This is the slope of the water table or potentiometric surface. A steeper gradient results in faster groundwater flow.
• Porosity and Permeability: As mentioned before, these properties influence how easily groundwater can move. Higher permeability means faster movement.
• Temperature and Viscosity of Water: Water tends to move faster in warmer conditions as it becomes less viscous.

Aquifers have various flow paths, which contribute to the diffusion and spreading of groundwater. This movement plays an essential role in replenishing surface waters and supporting ecosystems dependent on consistent water supplies.

Flow Rate Calculations

Calculating the flow rate of groundwater involves understanding how long it takes for water to travel a certain distance within an aquifer. This involves using the formula:\[ ext{Time} = \frac{\text{Distance}}{\text{Rate}}\]This formula is straightforward yet fundamental in problems related to groundwater flow. In our case, the exercise involved determining the time for groundwater to travel 24 meters at a rate of 0.4 meters per day.
To perform such calculations:

• Identify Known Variables: Establish the rate of flow and the distance over which groundwater is moving. Here, the rate is 0.4 meters per day, and the distance is 24 meters.
• Substitute Values: Place these values into the formula to solve for the unknown, which is the time in this instance.
• Calculate: The result of dividing the distance by the rate provides the time. As shown, 24 meters divided by 0.4 meters per day results in 60 days.

Understanding these basic calculations can help in managing water resources effectively and predicting how groundwater flows in response to natural and human-induced changes.