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Water is flowing in a pipe with a varying cross-s…

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Problem 42 Medium Difficulty

At a point where an irrigation canal having a rectangular cross section is 18.5 $\mathrm{m}$ wide and 3.75 $\mathrm{m}$ deep, the water flows at 2.50 $\mathrm{cm} / \mathrm{s} .$ At a point downstream, but on the same level, the canal is 16.5 $\mathrm{m}$ wide, but the water flows at 11.0 $\mathrm{cm} / \mathrm{s} .$ How
deep is the canal at this point?

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Video Transcript

Okay, So the crux of this problem is recognizing that the flow of water is conserved throughout the canal, and so of this's captured by the Continuity equation, which says that the cross sectional area times the velocity of the water at one point is equal to the cross sectional area times the velocity at another point. So basically, at the area decreases, the water has to flow faster. And this is to prevent, um But like if this equation wasn't satisfied than water would be bunching up at one point or spreading out another point, or is we want the flow to be smooth and continuous. So in the first part of the canal were given that the dimensions or 18.5 and 3.75 So this wolf this combined factors served services are a one, and this serves is our V one and um 16.5 times the unknown that it would be our eight to and the 11 centimeters per second would be R V two. So since we want to solve this equation for a H, it's simply going to be 18.5 times 3.75 times 2.5 over 16.5 times 11. Now it might seem inconsistent that we're using centimeters for the velocity and meters for the dimensions of the canal. But because we divide the one by V two, the's length units cancel out, and we don't actually have to worry about doing a conversion.

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Problem

Water is flowing in a pipe with a varying cross-s…

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Video Transcript

Hugh D. Young

College Physics

Christina Krawiec

Andy Chen

Liev Birman

Zachary Mitchell

This textbook answer is only visible when subscribed! Please subscribe to view the answer

College Physics

Christina Krawiec

Andy Chen

Liev Birman

Zachary Mitchell

Hugh D. YoungCollege Physics

Christina Krawiec

Andy Chen

Liev Birman

Zachary Mitchell

Hugh D. Young

College Physics