Calculating Water Level Rise in Trapezoid Trough

In summary, the water level rise in a trapezoid trough is calculated using a mathematical formula that takes into account the volume of water and the dimensions of the trough. The factors that affect water level rise include the volume of water, dimensions of the trough, slope of the trough's walls, and any irregularities in the trough's shape. The water level rise can be accurately predicted, but may differ slightly from the actual water level due to factors like evaporation and seepage. To control the water level rise, the dimensions and slope of the trough can be adjusted. However, safety concerns should be considered, such as ensuring the trough is structurally sound and taking caution when making adjustments.
  • #1
rocomath
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Homework Statement


A water trough is 10m long and a cross-section has a shape of an isosceles trapezoid that is 30cm wide at the bottom, 80cm wide at the top, and has a height of 50cm. If the bottom of the trough is being filled with water at the rate of .2m^3/min, how fast is the water level rising when the water is 30cm deep?


Homework Equations


A (trapezoid) = .5(b1+b2)


The Attempt at a Solution


http://img218.imageshack.us/img218/5321/22806877ce9.jpg
 
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  • #2
nvm i got it, my geometry isn't that great but i pulled through!
 

Related to Calculating Water Level Rise in Trapezoid Trough

1. How is the water level rise calculated in a trapezoid trough?

The water level rise in a trapezoid trough is calculated by using the formula:
h = (V - bL) / ((a + c)L)
Where:
h = water level rise
V = volume of water
b = bottom width of trough
L = length of trough
a = top width of trough
c = distance between bottom width and top width of trough

2. What are the factors that affect water level rise in a trapezoid trough?

The factors that affect water level rise in a trapezoid trough include the volume of water, the dimensions of the trough (bottom and top width, length), and the slope of the trough's walls. Additionally, any obstacles or irregularities in the trough's shape can also affect the water level rise.

3. Can the water level rise be accurately predicted in a trapezoid trough?

Yes, the water level rise can be accurately predicted in a trapezoid trough by using the appropriate mathematical formula and considering all the factors that may affect the water level. However, it is important to note that the predicted water level rise may differ slightly from the actual water level due to factors such as evaporation and seepage.

4. How can the water level rise in a trapezoid trough be controlled?

The water level rise in a trapezoid trough can be controlled by adjusting the dimensions of the trough, such as the bottom and top width, and the length. By increasing the dimensions, the trough can hold more water and result in a higher water level rise. Additionally, the slope of the trough's walls can also be adjusted to control the water level.

5. Are there any safety concerns when calculating water level rise in a trapezoid trough?

Yes, there are safety concerns that should be considered when calculating water level rise in a trapezoid trough. It is important to ensure that the trough is structurally sound and can handle the weight of the water without collapsing. Additionally, caution should be taken when adjusting the dimensions or slope of the trough to avoid accidents or injury.

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