MathMaster logo

MathMaster

  1. Home
  2. general
  3. 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
Adonis
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)
Math Question: What is the volume of a rectangular solid if the length is 6 cm, width is 4 cm, and height is 3 cm?
+
What is the equation of a hyperbola with center(2,-3), vertices at (2,-5) and (2,-1), and foci at (2,-7) and (2,1)?
+
What is the dimension of the vector space spanned by [1, -2, 3] and [2, -4, 6]?
+
New questions in Mathematics
Calculate to represent the function whose graph is a line that passes through the points (1,2) and (−3,4). What is your slope?
1 + 1
90 divided by 40
The profit G of the company CHUNCHES SA is given by G(x) = 3×(40 – ×), where × is the quantity of items sold. Find the maximum profit.
Which of the following is the product of multiplying twenty-seven and twenty-five hundredths by nine and twenty-seven hundredths?
In a normally distributed data set a mean of 31 where 95% of the data fall between 27.4 and 34.6, what would be the standard deviation of that data set?
Estimate the fifth term if the first term is 8 and the common ratio is -1/2
In the telephone exchange of a certain university, calls come in at a rate of 5 every 2 minutes. Assuming a Poisson distribution, the average number of calls per second is: a) 1/8 b) 1/12 c) 1/10 d) 2/5 e) 1/24
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)
A researcher is interested in voting preferences on change of the governing constitution in a certain country controlled by two main parties A and B. A questionnaire was developed and sent to a random sample of voters. The cross tabs are as follows Favour Neutral Oppose Membership: Party A 70 90 85 Party B 50 50 155 Test at α = 0.05 whether party membership and voting preference are associated and state the conditions required for chi-square test results to be valid.
cube root of 56
2X+2=8
A person runs 175 yards per minute write a variable that represents the relationship between time and distance
Find the vertex F(x)=x^2-10x
A psychologist is investigating the levels of test anxiety in various university courses. Anxiety is measured on a scale ranging from 0 to 100, where 0 indicates the complete absence of anxiety and 100 represents an extreme level of anxiety. From the data obtained, it has been discovered that the psychology score is triple that of nursing, and in turn, the latter has a score 10 points lower than the nutrition major. Furthermore, the score in the veterinary degree is 15 points higher than that of nutrition. Finally, if we add the scores of all the races, we will obtain a total of 173 points. Pose the equation that represents the situation described in the previous problem and determine: What is the score that psychology obtained regarding its anxiety level before the exams?
Find I (Intrest) using simple interest formula of 17700 @ 15% for 4 years
2x-4=8
8(x+4) -4=4x-1
If the area of a circle is 75.7ft2, what is the radius? Give the answer in metres. Round answer to 2 decimal places and enter the units.
Matilde knows that, when driving her car from her office to her apartment, she spends a normal time of x minutes. In the last week, you have noticed that when driving at 50 mph (miles per hour), you arrive home 4 minutes earlier than normal, and when driving at 40 mph, you arrive home 5 minutes earlier later than normal. If the distance between your office and your apartment is y miles, calculate x + y.

You might be interested in