Title Ch 12 HW Physics & Mathematics Physics Mechanics Physical Sciences 2.3 MB 33
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3/8/2017 Ch 12 HW

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Hint 1. General approach: considerations on fluid mechanics

By restricting the area across which the water is flowing, Isabella forces the water to flow out at a higher speed.

After estimating the initial velocity that the water must have in order to reach a distance of 10 meters, you can

determine the cross-sectional area of the hose hole that corresponds to such an initial velocity of the water by

applying the continuity equation.

Hint 2. Find the outflow speed needed

Find the initial speed that the water should have in order to reach a distance of 10 meters. Consider the water

flowing out of the hose as composed of independent particles in projectile motion. Recall that projectile motion is

described as a combination of horizontal motion with constant velocity and vertical motion with constant

acceleration. Note that the hose is pointed parallel to the ground, so the initial velocity of water is purely horizontal.

Thus .

Express your answer numerically in meters per second to three significant figures.

Hint 1. Projectile motion

If the effects due to air resistance are ignored, as they should be in this problem, the motion of a projectile

can be analyzed as a combination of horizontal motion with constant velocity and vertical motion with

constant acceleration.

Consider a particle undergoing projectile motion in the x-y  coordinate plane, with the x   axis horizontal and the

y  axis pointing vertically upward. Let and represent the components of the initial velocity of the

particle. Let and represent the initial horizontal and vertical positions of the particle. The equations

describing the position of the particle as a function of time are then

,

where is the magnitude of the acceleration due to gravity. In this part, you are asked to find the outflow

speed, which is horizontal, and thus corresponds to is the above equation. Consider carefully what the

values of the other constants -- , , and --are.

Hint 3. Find the cross-sectional area needed

Once you know the horizontal velocity of the water that would be needed for the emerging stream to reach a

distance of 10 meters, find the cross-sectional area that corresponds to that outflow speed.

Ass ume that the flow rate remains steady after the partial blockage of the hose hole, so that the continuity equation

applies.

Hint 1. Apply the continuity equation

In an incompressible fluid moving steadily, the mass of fluid flowing along a flow tube is constant. In

particular, consider a flow tube between two stationary cross sect ions with areas and . Let the fluid

speeds at these sections be and , respectively. Then conservation of mass takes the form

,

= 22.1

Typesetting math: 70%

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3/8/2017 Ch 12 HW

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which is known as the continuity equation.

If initially the water is flowing through the hose of cross-sectional area at a speed , and you want it to

flow through a smaller area at a higher speed , what should the new cross-sectional area of the hose be?

Correct

Exercise 12.37

Water is flowing in a circular pipe varying cross-sectional area, and at all points the water completely fills the pipe.

Part A

At one point in the pipe t he radius is 0.245 . What is the speed of the water at this point if water is flowing into this pipe

at a steady rate of 1.85 ?

Correct

Part B

At a second point in the pipe t he water speed is 2.30 . What is the radius of the pipe at this point?

Correct

=

= 1.12

= 84 %

= 9.81

= 0.506

Typesetting math: 70%