$MathMaster logo$

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

104 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)

Question: "What is the x-intercept of the quadratic function y = 2x^2 + 5x - 3?"

+

Question: In how many ways can a committee of 4 members be formed from a group of 10 students?

+

What are the asymptotes of the hyperbola given by the equation (x^2/36) - (y^2/16) = 1?

+

New questions in Mathematics

A sample is chosen from a population with y = 46, and a treatment is then administered to the sample. After treatment, the sample mean is M = 47 with a sample variance of s2 = 16. Based on this information, what is the value of Cohen's d?

Let the vectors be u=(-1,0,2) , v=(0,2,-3) , w=(2,2,3) Calculate the following expressions a)<u,w> b) <2u- 5v,3w>

-442/c+5=26 what is c?

Eight acts are scheduled to perform in a variety show how many different ways are there to schedule their appearances show your work

Since one of the three integers whose product is (-60) is (+4), write the values that two integers can take.

Kayla has $8,836.00 in her savings account. The bank gives Kayla 5%of the amount of money in account as a customer bonus. What amount of money does the bank give Kayla? Justify your answer on a 6th grade level.

The data set (75, 85, 58, 72, 70, 75) is a random sample from the normal distribution No(µ, σ). Determine a 95% two-sided confidence interval for the mean µ .

Suppose the horses in a large they will have a mean way of 818 pounds in a variance of 3481. What is the probability that the mean weight of the sample of horses with differ from the population mean by more than 18 pounds is 34 horses are sampled at random from the stable.

The durability of a tire of a certain brand is a Normal random variable with an average of 64,000 km and a standard deviation of 9,000 km. Assuming independence between tires, what is the probability that the 4 tires on a car will last more than 58,000 km?

6-35 A recent study by an environmental watchdog determined that the amount of contaminants in Minnesota lakes (in parts per million) it has a normal distribution with a mean of 64 ppm and variance of 17.6. Assume that 35 lakes are randomly selected and sampled. Find the probability that the sample average of the amount of contaminants is a) Greater than 72 ppm. b) Between 64 and 72 ppm. c) Exactly 64 ppm. d) Greater than 94 ppm.

Engineers want to design seats in commercial aircraft so that they are wide enough to fit 95% of all males. (Accommodating 100% of males would require very wide seats that would be much too expensive.) Men have hip breadths that are normally distributed with a mean of 14.4 in. and a standard deviation of 1.2 in. Find P95. That is, find the hip breadth for men that separates the smallest 95% from the largest 5%.

Three machines called A, B and C, produce 43%, 26% and 31% of the total production of a company, respectively. Furthermore, it has been detected that 8%, 2% and 1.6% of the product manufactured by these machines is defective. a) What is the probability that a product is not defective? b) A product is selected at random and found to be defective, what is the probability that it was manufactured on machine B?

A Smooth Plane is listed for $195.00. Discounts of 12% and 10% are allowed. If the customer pays cash within 30 days, an additional discount of 3% is granted. What is the cost if a carpenter takes advantage of all the discounts offered?

Build a truth table for the statement ~(pvq)^~p

Let x be an integer. Prove that x^2 is even if and only if is divisible by 4.

In a 24 hours period, the average number of boats arriving at a port is 10. Assuming that boats arrive at a random rate that is the same for all subintervals of equal length (i.e. the probability of a boat arriving during a 1 hour period the same for every 1 hour period no matter what). Calculate the probability that more than 1 boat will arrive during a 1 hour period. (P(X>1) ) Give your answers to 4 decimal places and in a range between 0 and 1

Let G be the center of gravity of triangle ABC. We draw through A a parallel to BC on which we take a point D so that DG⊥BG. If the area of the quadrilateral AGBD is equal to s, show that AC·BD≥2·s.

1. The cost to transport 250 packages of cement 120 kilometers is $600. What will be the cost to transport 500 packages 300 kilometers?

In an experiment to assess the effect of listening to audiobooks while driving, participants were asked to drive down a straight road in a driving simulator. The accompanying data on time (in milliseconds) to react when a pedestrian walked into the street for 10 drivers listening to an audiobook are consistent with summary statistics and graphs that appeared in the paper "Good Distractions: Testing the Effect of Listening to an Audiobook on Driving Performance in Simple and Complex Road Environments."† (Round your answers to four decimal places.) 1,018 1,007 1,054 988 937 1,030 1,065 1,011 860 1,106 A button hyperlink to the SALT program that reads: Use SALT. Calculate the variance for this data set. 7437.7333 Incorrect: Your answer is incorrect. Calculate the standard deviation for this data set. 86.2022 Incorrect: Your answer is incorrect.