1) Consider a uniform, rectangular channel with width b and no bottom slope,through which water is flowing in the shallow-water regime, i.e. the waves arelong compared to the water's depth h.• Write the equations for conservation of mass and x-momentum in a rainyday, when a volume r(x, t) of water falls on the channel per unit surfaceand unit time (Notice that the rain brings no horizontal momentum, andneglect any possible effect that its vertical momentum may have on thepressure at the water's surface.)• Manipulate your equations into an equation for hi and one for ut, whereh(x, t) is the water's height and u(x, t) is its mean velocity in the x direc-tion.• Interpret the meaning of the term that appears as a forcing in the equationfor ut, considering for simplicity solutions (and rain) that do not depend onx. (Hint: you may want to compare the total momentum in an arbitrarysegment of the channel at two times separated by a small interval At.)

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1) Consider a uniform, rectangular channel with width b and no bottom slope, through which water is flowing in the shallow-water regime, i.e. the waves are long compared to the water's depth h. • Write the equations for conservation of mass and x-momentum in a rainy

1) Consider a uniform, rectangular channel with width b and no bottom slope, through which water is flowing in the shallow-water regime, i.e. the waves are long compared to the water's depth h. • Write the equations for conservation of mass and x-momentum in a rainy

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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