A liquid flowing from a vertical pipe has a definite shape as it flows from the pipe. To get the equation for this shape, assume that the liquid is in free fall once it leaves the pipe. Just as it leaves the pipe, the liquid has speed ν 0 and the radius of the stream of liquid is r 0 . (a) Find an equation for the speed of the liquid as a function of the distance y it has fallen. Combining this with the equation of continuity, find an expression for the radius of the stream as a function of y . (b) If water flows out of a vertical pipe at a speed of 1.20 m/s, how far below the outlet will the radius be one-half the original radius of the stream?
A liquid flowing from a vertical pipe has a definite shape as it flows from the pipe. To get the equation for this shape, assume that the liquid is in free fall once it leaves the pipe. Just as it leaves the pipe, the liquid has speed ν 0 and the radius of the stream of liquid is r 0 . (a) Find an equation for the speed of the liquid as a function of the distance y it has fallen. Combining this with the equation of continuity, find an expression for the radius of the stream as a function of y . (b) If water flows out of a vertical pipe at a speed of 1.20 m/s, how far below the outlet will the radius be one-half the original radius of the stream?
A liquid flowing from a vertical pipe has a definite shape as it flows from the pipe. To get the equation for this shape, assume that the liquid is in free fall once it leaves the pipe. Just as it leaves the pipe, the liquid has speed ν0 and the radius of the stream of liquid is r0. (a) Find an equation for the speed of the liquid as a function of the distance y it has fallen. Combining this with the equation of continuity, find an expression for the radius of the stream as a function of y. (b) If water flows out of a vertical pipe at a speed of 1.20 m/s, how far below the outlet will the radius be one-half the original radius of the stream?
two satellites are in circular orbits around the Earth. Satellite A is at an altitude equal to the Earth's radius, while satellite B is at an altitude equal to twice the Earth's radius. What is the ratio of their periods, Tb/Ta
Fresnel lens: You would like to design a 25 mm diameter blazed Fresnel zone plate with a first-order power of
+1.5 diopters. What is the lithography requirement (resolution required) for making this lens that is designed
for 550 nm? Express your answer in units of μm to one decimal point.
Fresnel lens: What would the power of the first diffracted order of this lens be at wavelength of 400 nm?
Express your answer in diopters to one decimal point.
Eye: A person with myopic eyes has a far point of 15 cm. What power contact lenses does she need to correct
her version to a standard far point at infinity? Give your answer in diopter to one decimal point.
Paraxial design of a field flattener. Imagine your optical system has Petzal curvature of the field with radius
p. In Module 1 of Course 1, a homework problem asked you to derive the paraxial focus shift along the axis
when a slab of glass was inserted in a converging cone of rays. Find or re-derive that result, then use it to
calculate the paraxial radius of curvature of a field flattener of refractive index n that will correct the observed
Petzval. Assume that the side of the flattener facing the image plane is plano. What is the required radius of
the plano-convex field flattener? (p written as rho )
Chapter 12 Solutions
University Physics with Modern Physics (14th Edition)
Chemistry: An Introduction to General, Organic, and Biological Chemistry (13th Edition)
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