A lake is fed by a stream with a constant flow rate of 1000 ft³/s. Water evaporates at a constant rate of 10 ft³/s per square mile of surface area. The surface area of the lake, Asurface, varies with h (in ft) according to the equation Asurface = 4 mi² +5(mi² / ft) · h : Assuming there is no drainage from the lake, determine: a) the rate of change of the volume in the lake if the depth is 19ft b) the steady-state depth of water in the lake

A lake is fed by a stream with a constant flow rate of 1000 ft³/s. Water evaporates at a constant rate of 10 ft³/s per square mile of surface area. The surface area of the lake, Asurface, varies with h (in ft) according to the equation Asurface = 4 mi² +5(mi² / ft) · h : Assuming there is no drainage from the lake, determine: a) the rate of change of the volume in the lake if the depth is 19ft b) the steady-state depth of water in the lake

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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Applied Fluid Mechanics

A fluid is a substance that is continuously deformed by the application of shear stress. The rate of deformation of a fluid depends on its viscosity. The fluid tries to flow when it interacts with some other system.

Question

Problem 6.1
A lake is fed by a stream with a constant flow rate of 1000 ft³/s. Water evaporates at a constant
rate of 10 ft³/s per square mile of surface area. The surface area of the lake, Asurface, varies with h
(in ft) according to the equation
Asurface = 4 mi² +5(mi² / ft) · h
Assuming there is no drainage from the lake, determine:
a) the rate of change of the volume in the lake if the depth is 19ft
b) the steady-state depth of water in the lake
Answers: (a) 8 ft³/sec <dv/dt < 12 ft³/sec; (b) 18 ft <h < 20 ft

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