Initial Publication Date: August 11, 2023

Solving Math Word Problems - Practice Problems
Solving Earth science word problems with GFSE

This module is available for public use, but it is undergoing revision after classroom implementation with the Math Your Earth Science Majors Need project.

Hydrology (surface water)

There is a significant amount of math used to represent the movement of water in Hydrology (volume, rates). In fact, many Hydrology courses are built on the foundation of the conservation equations for mass and energy! You may recall these from early science classes, "Matter cannot be created nor destroyed," and the same can be said for energy.

Problem 1: A rectangular weir is placed in a small stream to measure flow. The value of L is 1.5 ft and H is 0.22 ft. Compute the discharge of the stream.

 

Who cares? Measuring stream flow can be time-consuming and even dangerous, even in small streams.  The construction of a weir makes it much easier to measure, quantify, and report flow.  It's a permanent structure that saves time and money.  Additionally, these flow values are important for understanding stream water chemistry, aquatic habitat conditions, and changes within the watershed upstream of the weir.

Engineering geology

It is essential to consider the strength of the ground and the weight of buildings, in order to build safe buildings. It is critically important to understand the stresses and disruption that the Earth can cause on the human-built world and how human structures can impact the ground below. The scientists and engineers that work on this subject consider things such as force and pressure to make sure structures will be stable.

Problem 2: The Empire State Building in New York City has a mass of 3.3 x 108 kilograms (kg) and sits on a foundation footprint of about 90 m x 90 m. What is the force exerted on the foundation in Newtons (N)? What is the pressure applied to the foundation in Kilopascals (KPa)?


Geomorphology

The study of landscapes and especially the response of the land surface to exposure to the elements is called Geomorphology. It mainly focuses on studying the more recent past, the processes that have shaped our current landscape. It deals with the interaction of rocks and soil with the hydrosphere and atmosphere. Using math to analyze and model the processes and rates of weathering, erosion, transportation, and deposition is important for science and engineering. We can mitigate geologic hazards, determine appropriate land use, and remediate environmental damage by better-understanding the land and the forces that shape it.

Problem 3: What is the wavelength (in meters) and velocity (in meters per second) of a wave created by a storm in the Gulf of Mexico, if the wave period (T) is 5 seconds.

 

Who cares? While these numbers may seem uninteresting or unimportant, knowing the wavelength and velocity of waves is essential to determining their potential for erosion and damage along coastlines. Wave action is persistent, occurring continuously over the course of time as wind changes speed and direction, changing the impact of water against a rocky or sandy shoreline. But it can also be catastrophic in the case of hurricanes and major storms. Consider a developed beach and how important it might be to know the expected HEIGHT of waves on shore measured by open ocean buoys! While wavelength and wave velocity aren't inherently troubling on their own, they are necessary to calculate the wave height, which is dependent upon water DEPTH. But, if a home or business were built near shore, it would certainly be necessary to know how high waves would be expected during a storm to prepare and maybe even evacuate.

Sedimentology

Sedimentology is the science of the origin, movement, and deposition of sediments and often accompanies stratigraphy, the description and analysis of sedimentary layers. This critical course in a Geology degree combines principles of petrology and mineralogy, hydrology, and physics (among others) to help students understand Earth history and the processes that create Earth's sedimentary record. Sedimentology is especially important in resource exploration and extraction, as well as engineering. The following problem is related to the idea of flow regimes in a current that has implications for "entrainment", the picking up of material from a stream or lake bed, and transport that ultimately leads to deposition.

Problem 4: A small stream has a velocity of 1.5 m/s and an average depth of 0.38 m. Is this flow critical, subcritical, or supercritical? NOTE: The Froude number is the measure of a stream's criticality.  

Hydrology (groundwater)

Hydrology is sometimes taught as two separate courses, Surface Water (Hydrology) and Groundwater (Hydrogeology). Regardless, these courses are heavily based in physics and mathematics principles, dealing with the quantity and movement of water. Understanding groundwater systems is especially dependent on mathematics because we generally cannot "see" the system and are dealing with models and incomplete data.

Problem 5: A confined aquifer is 8 ft thick. The potentiometric surface drops 1.33 ft between two wells that are 685 ft apart. The hydraulic conductivity is 251 ft/day and the effective porosity is 0.27. What is the average linear velocity of flow through the system?

Who cares? Groundwater is a critical resource for human survival. Inland, and especially rural, areas, depend heavily on groundwater for drinking and irrigation, along with all of their other water needs. Not only is it important to understand the flow and velocity that water is traveling underground. But getting to the heart of water's behavior in the subsurface allows us to use these resources more sustainably. It also helps us to predict how contaminants may move through the ground and where they could emerge to cause problems for our ecosystems.

Next steps

TAKE THE QUIZ!!  

I think I'm competent with solving math problems and I am ready to take the quiz! This link takes you to WAMAP. If your instructor has not given you instructions about WAMAP, you may not have to take the quiz.

Or you can go back to the Solving Math Word Problems explanation page.