A hydrologist conducts a morphometric analysis on a river basin using a topographic map dr… — JAMB UTME

A hydrologist conducts a morphometric analysis on a river basin using a topographic map drawn at a scale of $1:25,000$ . Stream ordering reveals $28$ first-order streams, $7$ second-order streams, and $1$ third-order stream. If the total basin area measured on the map is $32\text{ cm}^2$ , what is the stream frequency ( $F_s$ ) of the basin in $\text{streams per km}^2$ ?

Answer: 18 streams/km^2

Answer

The stream frequency of the river basin is

18\text{ streams per km}^2

To determine stream frequency (

F_s

), first calculate the total stream count (

N = 28 + 7 + 1 = 36

). Next, convert the map area of

32\text{ cm}^2

to actual ground area using the scale

1:25,000

. Since

1\text{ cm}

on the map represents

0.25\text{ km}

1\text{ cm}^2

represents

0.0625\text{ km}^2

. Multiplying

32\text{ cm}^2

0.0625\text{ km}^2/\text{cm}^2

gives a basin area of

2.0\text{ km}^2

. Finally, divide the total number of streams by the basin area (

36 / 2.0 = 18\text{ streams per km}^2

Step-by-Step Solution

Sum the number of streams of each order to find the total stream count (

N

N = 28 + 7 + 1 = 36\text{ streams}

Stream frequency considers the entire stream network comprising all stream orders in the basin.

Convert map area to ground area using the map scale (

1:25,000

1\text{ cm} = 0.25\text{ km} \implies 1\text{ cm}^2 = 0.0625\text{ km}^2

. Actual Area

A = 32 \times 0.0625 = 2.0\text{ km}^2

Stream frequency must be expressed per unit of actual ground area in

\text{km}^2

rather than map area.

Divide total number of streams by actual basin area.

F_s = \frac{36}{2.0} = 18\text{ streams/km}^2

Stream frequency (

F_s

) is defined as the ratio of total number of streams to the drainage basin area.

Key Concept

Stream Frequency (

F_s

) Calculation in River Basin Morphometry

Estimated Time:2m 0s

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