Three Point Problems 4

Groundwater Gradient Exercise

Groundwater Gradient Exercise

Geology 210Objectives:In this lab we will perform the following tasks:

1) Measure water levels in six wells located on the edge of the CSUS campus.

2) Plot the results from shallow and deep wells on two different maps.

3) Construct three point problems to determine the direction of groundwater flow

in shallow and deep wells.4) Write a technical report that summarizes results.Equipment needed:Ruler or engineering scale, calculator

Todays exercise:1) Measure water levels in the three shallow wells and three deep wells. These water levels must then be converted to elevations above or below sea level (note: the common abbreviation for sea level is MSL or Mean Sea Level). Use the following formula to calculate the elevation of the water table above or below sea level:

(Land surface elevation) - (Measured water level) = Elevation (MSL)

Record your results on this table:

Well numberLand surface elevation (surveyed elevation at top of casing) Measured water level in well (from land surface to water table)Elevation of water table (MSL)

MW-1

MW-1A

MW-2

MW-2A

MW-3A

MW-3A

2) Plot the water levels (MSL) for the shallow wells on the map labeled Shallow wells". Plot the water levels (MSL) for the deep wells on the map labeled Deep wells".

3) Construct a graphical three-point problem to determine the direction of groundwater flow for each of the maps. Remember that groundwater flows down-gradient (down-hill), so the water will flow from a higher elevation toward a lower elevation. Be careful with positive and negative numbers in this part of the exercise. A positive number is an elevation above sea level, and a negative number is an elevation below sea level.

The three point problem is based on a simple principle of geometry: three points define a plane, and if you can define the position of a plane in space you can also determine the dip (inclination) of the plane. Because groundwater flows down-gradient, it will flow in the direction of dip of the plane. "Three point problems" didasari dari prinsip-prinsip geometri : "three points" mendefinisikan sebuah bidang, dan ketika anda dapat mendefinisikan posisi dari bidang pada ruang, anda juga dapat menentukan dip ( inklinasi ) dari bidang. Karena airtanah mengalir ke bawah gradien, airtanah akan mengalir sesuai arah dip pada bidang Use the following example to help you work through your three point problems for the shallow and deep wells:

ay, dibawah ini langkah2nya buat gambar pake metode 3 point tadi, kalau mau ditranslatetin bilang lintang ay .

Sample problem: Follow steps 1-4 to solve this example of a three point problem:

Contoh permasalahan : Ikuti langkah 1 sampai dengan 4 untuk menyelesaikan permasalahan dengan metode three point problem :

Step1) Draw a line between the highest and lowest groundwater elevations. Remember to use elevations that are corrected (compared) to sea level.Langkah 1.

Gambarlah sebuah garis diantara elevasi( ketinggian?) airtanah tertinggi dan ketinggian airtanah terendah. Ingatlah untuk menggunakan ketinggian yang dikoreksi ( dibandingkan ) dengan permukaan air laut.

Step 2) Langkah 2.a. Determine the position where the intermediate groundwater elevation would project along this line. Use measured distances on the map and differences between water level elevations to construct a ratio and determine this position:a. Tentukan dimana posisi ketinggian intermediate airtanah yang akan diproyeksikan disepanjang garis ini. Gunakan jarak yang telah diukur pada peta dan perbedaan antara ketinggian muka air untuk menentukan rasio dan menentukan posisi.b. Read the highest elevation, lowest elevation and intermediate elevation from your map, and plug these values into the ratio equation. Use your ruler to measure the distance between the highest and lowest elevations on your map and plug this value into the equation. Any units are will work, but millimeters or metric units are often easiest to use. Solve for the unknown distance. The unknown distance is the map distance from the highest elevation to the intermediate elevation.Example ratio equation:

(highest elevation - intermediate elevation) = unknown distance (highest elevation - lowest elevation)

(measured distance between

highest and lowest elevations)b. Bacalah ketinggian tertinggi, ketinggian terendah, dan ketinggian intermediate dari peta anda, dan masukkan nilai-nilai tersebut dalam persamaan rasio. Gunakan penggaris untuk mengukur jarak antara ketinggian tertinggi dan terendah dalam peta dan masukkan nilai-nilai tersebut dalam persamaan. Semua satuan dapat digunakan, namun satuan milimeter atau satuan metrik lebih mudah untuk digunakan. Selesaikan persamaan untuk mendapatkan nilai jarak yang belum diketahu. Jarak yang belum diketahui tersebut merupakan jarak peta dari ketinggian tertinggi ke ketinggian intermediet. Persamaan rasio :

(Ketinggian tertinggi - ketinggian intermediet) = Jarak yang belum diketahui (Ketinggian tertinggi - Ketinggian terendah )

(Jarak yang telah diukur antara

ketinggian tertinggi dan terendah )

a.Penyelesaian :

x = 94.6 mm.Step 3) Mark the unknown distance that you calculated in step 2 along the line that connects the highest and lowest elevations. Make sure that you start measuring from the highest elevation.Langkah 3.

Tandai Jarak yang belum diketahui(x) yang telah anda hitung pada langkah 2, tarik garis yang menghubungkan dari ketinggian tertinggi ke ketinggian terendah. Pastikan anda menarik garis dari ketinggian tertinggi.

Step 4) Draw a line between the intermediate elevation and the unknown point that you marked in step 3. This new line is perpendicular to the dip (inclination) of the groundwater surface. It is essentially an equipotential line (a line in an two-dimensional field where the total hydraulic head or water level is constant for all points on the line). Draw a large arrow perpendicular to your new line to represent the dip of the groundwater surface and the direction of groundwater flow. The direction of groundwater flow is 90( to the equipotential line.Langkah 4.Gambar sebuah garis diantara ketinggian intermediet dan titik (x) yang telah anda tandai sebelumnya pada langkah 3. garis baru ini tegak lurus terhadap dip ( inklinasi ) dari permukaan airtanah. Garis ini pada dasarnya adalah garis ekuipotensial ( sebuah garis dalam bidang dua dimensi dimana total ketinggian hidrolik ( disini "head"kalau menurut lintang itu satuan ketinggian ay, soalnya lintang belajar di mekanika fluida, untuk british, satuan untuk persamaan panjang itu bisa dalam bentuk yang namanya bentuk "head" ) atau ketinggian air adalah konstan untuk semua titik dalam garis ) . Gambar sebuah panah besar yang tegak lurus dengan garis antara ketinggian intermediate dan titik (x) tadi, untuk mewakili dip permukaan air tanah dan arah aliran dari airtanah. Arah aliran airtanah sebesar 90( dari garis ekuipotensial.

Figure 2: Map of shallow wells, CSUS wellfield.

Figure 3: Map of deep wells, CSUS wellfield. Ketinggian terendah

= fine sandy unconfined aquifer

Garis Ekuipotensial

Ketinggian Intermediate

Ketinggian Tertinggi

75 ft

50 ft

200 ft

Confining layer

Shallow unconfined aquifer

Shallow Monitoring

Wells

100

50

0

Feet

Feet

150

200

100

50

0

Deep confined aquifer

Extraction

Well

Deep Monitoring

Wells

= silty clay confining layer

= coarse sandy interval

Figure 1: Cross-section of the CSUS wellfield, showing location and depths of shallow and deep wells.

Schematic cross section of on-campus wellfield at California State University, Sacramento

Jarak yang telah diukur = 114 mm.

Ketinggian Intermediate

Ketinggian Terendah

Ketinggian Intermediate

Ketinggian Terendah

KetinggianTertinggi

75 ft

50 ft

200 ft

Ketinggian Tertinggi

75 ft

(200 ft - 50 ft) 114 mm.

Jarak yang belum diketahui (x)

=

(200 ft - 75 ft)

50 ft

200 ft

200 ft

50 ft

75 ft

Ketinggian tertinggi

Ketinggian terendah

Ketinggian Intermediate

Jarak yang belum diketahui (x) = 94.6 mm.

Tandai posisi jarak (x)

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