$MathMaster logo$

MathMaster

Home
general
a river basin has an average annual precipitation of 2500 mm year and a drainage area of 10000 km2 the average discharge a

Question

A river basin has an average annual precipitation of 2500 mm/year and a drainage area of 10000 km2. The average discharge at the outlet of the basin is 200 m3/s. What is the average evapotranspitation (mm/year) in this region? What is the runoff coefficient? Assuming that the basin has average precipitation and a constant runoff coefficient, estimate the average discharge in a subbasin of 2000 km2.

81

likes

403 views

Answer to a math question A river basin has an average annual precipitation of 2500 mm/year and a drainage area of 10000 km2. The average discharge at the outlet of the basin is 200 m3/s. What is the average evapotranspitation (mm/year) in this region? What is the runoff coefficient? Assuming that the basin has average precipitation and a constant runoff coefficient, estimate the average discharge in a subbasin of 2000 km2.

$Expert avatar$

4.4

106 Answers

\text{PQ} = \text{Precipitação} \times \text{Área de drenagem}

= 2500 \frac{\text{mm}}{\text{ano}} \times 10000 \text{km}^2

= \left(2500 \times 10^{-3} \frac{\text{m}}{\text{ano}} \right) \times \left(10000 \times 10^6 \text{m}^2\right)

= 25000 \times 10^3 \text{m}^3/\text{ano}

= 2.5 \times 10^{10} \text{m}^3/\text{ano}

Q = \text{Vazão} \times \text{Tempo}

= 200\frac{\text{m}^3}{\text{s}} \times (365 \times 24 \times 60 \times 60)\frac{\text{s}}{\text{ano}}

= 200 \frac{\text{m}^3}{\text{s}} \times 31536000 \frac{\text{s}}{\text{ano}}

= 6.3072 \times 10^9 \text{m}^3/\text{ano}

ET = \text{What we need to calculate} = PQ - Q

= 2.5 \times 10^{10} - 6.3072 \times 10^9 \text{m}^3/\text{ano}

= 1.86928 \times 10^{10} \text{m}^3/\text{ano}

To transform the result to mm (per year), divide it by the area again and then express in mm/year.

ET = \frac{1.86928 \times 10^{10} \text{m}^3/\text{ano}}{10^7 \text{m}^2}

ET = 1869.28 \text{mm/ano}

Coeficiente de escoamento = \frac{\text{Q}}{PQ}

= \frac{6.3072 \times 10^9 \text{m}^3/\text{ano}}{2.5 \times 10^{10} \text{m}^3/\text{ano}}

= 0.2523

Now calculating average flow for a sub-basin of 2000 km^2:

Q_{sub} = Coeficiente de escoamento \times PQ_{sub}

= 0.2523 \times (2500 \times 10^{-3} \frac{\text{m}}{\text{ano}} \times 2000 \times 10^6 \text{m}^2)

= 0.2523 \times (5 \times 10^9 \text{m}^3/\text{ano})

= 1.2615\times 10^9 \text{m}^3/\text{ano}

Convert this to m^3/s:

Q_{sub}= \frac{1.2615\times 10^9 \frac{\text{m}^3}{\text{ano}}}{365 \times 24 \times 60 \times 60 \text{s}}

= \frac{1.2615\times 10^9}{31536000} \frac{\text{m}^3}{\text{s}}

≈ 40 \text{m}^3/\text{s}

Frequently asked questions (FAQs)

What is 3/8 of a number, when the number is equal to 160?

+

What is the equation of the square root function with a vertex at (2, -3)?

+

What is the value of sin(A) if A is an acute angle in a right triangle with an opposite side of length 5 and a hypotenuse of length 13?

+

New questions in Mathematics

Add. 7/w²+18w+81 + 1/w²-81

What is the amount of interest of 75,000 at 3.45% per year, at the end of 12 years and 6 months?

a) A tap can supply eight gallons of gasoline daily to each of its 250 customers for 60 days. By how many gallons should each customer's daily supply be reduced so that it can supply 50 more customers for twenty more days?

The length and breadth of my rectangular vegetable garden is 12,5m and 7,25m respectively. What is the perimeter of the garden?

Two numbers differ by 7, and the sum of their squares is 29. Find the numbers.

An integer is taken at random from the first 40 positive integers. What is the probability that the integer is divisible by 5 or 6?

A regional candy factory sells a guava roll at a price of $48, the monthly fixed costs amount to $125,000 and the variable cost for making a guava roll is $28. Determine: a) The equation of the total income from the production of guava rolls.

A vaccine has a 90% probability of being effective in preventing a certain disease. The probability of getting the disease if a person is not vaccinated is 50%. In a certain geographic region, 60% of the people get vaccinated. If a person is selected at random from this region, find the probability that he or she will contract the disease. (4 Points)

In an audience of 4000 people, 2 people are chosen, at random, to appear on stage. How many ways can the people be chosen?

Which of the methods below can be used to workout 95% of an amount? a. Dividing the amount 100 and multiply by 95 b. Working out 5% of the amount and taking it away from the full amount c. Dividing 95 by 100 and multiplying the answer by the amount d. Dividing the amount by 95 and then multiply by 100

Buffalo Company makes and sells shampoo. Each unit requires $1.40 labor costs, material costs per unit are $0.90 and other variable costs are $0.30. It sells shampoo for $4.45 to retailers. Fixed costs are $15,000. It sold 25,000 units in the current month. What is the Break-Even point in units? What is the Break-Even point in dollars? What is the contribution margin of Buffalo Company?

Calculate the area of the parallelogram with adjacent vertices (1,4, −2), (−3,1,6) 𝑦 (1, −2,3)

a) 6x − 5 > x + 20

To verify that a 1 kg gold bar is actually made of pure gold, a dynamometer is used to record the weight of the bar submerged in water and out of water. a) What would be the value of the weight of the ingot recorded by the dynamometer out of the water? b) What magnitude of thrust does the ingot receive when it is submerged? c) What would the weight of the ingot have to be when it is submerged? Data Pagua = 1000 kg/m³ Pagua= 19300 kg/m³

Identify the slope and y intercept y=11+2/3x

did an analysis of dropout from the nursing faculty at the Universidad Veracruzana. With a poblation of 122 students, it turned out that according to the gender data, the female sex predominates with 82%, and the male sex male is found with 12%. The main factors why students drop out are, first of all, "Not "re-enrolled" at 49%, second place "Personal reasons" at 20%, third place "change of school" in 11%, "lack of documents" and "economic reasons" in 7%, change of residence and lack of social service in 3%. Of this sample, how many students dropped out for other reasons?

(3.1x10^3g^2)/(4.56x10^2g)

A plant found at the bottom of a lake doubles in size every 10 days. Yeah It is known that in 300 days it has covered the entire lake, indicate how many days it will take to cover the entire lake four similar plants.