Fluid/Stream Que work shown need guidance

[jen333]

Homework Statement

A can is filled with water to a depth of 37cm. A hole 12 cm above the obttom of the can produces a stream that is directed at a 34 degree angle ave the horizontal. Find the range and max height of this stream.

Homework Equations

by kinetcs

The Attempt at a Solution

.

v=sqrt2gh
=sqrt 2x9.81x (0.37m-0.12m)
= 2.21m/s

using the angles to get the vertical velocity: 2.21m/sxsin34=1.26m/s

I then use the eqn vf^2=vi^2+2ad where a=g
ultimately getting 7.8cm which I add to the 12cm to get approx 20cm as max height

as for the range, am i able to use the same velocity except with the x-component velocity?


Anyways, I'm slightly confused now. Thanks for any help!

 

[nvn]

jen333: Generally always maintain four significant digits throughout all your intermediate calculations, then round only the final answer to three significant digits. Your stream maximum height looks correct, y2 = 19.82 cm. You are doing quite well, so far, except for a minor typographic mistake; the stream initial vertical velocity, neglecting exit minor head loss, would be v1y = v1*sin(theta) = (2.214 m/s)sin(34 deg) = 1.238 m/s. Yes, you would use the same stream initial velocity, v1, to compute the stream horizontal velocity, vx. Next, use one of your kinematics equations to compute the stream final vertical velocity, v3y, when the stream hits the ground. Hopefully this will get you started. Continue using the kinematics equations to solve the problem.

 

[Maurice M ben]

The x component of the velocity is already there: the x component is constante Vx=Vo*cos(angle), and it eqaution of the motion can be found easily: X=Vx(t)+Vo.
in terms of stream function you can use dy/dx=Vy/Vx

 

[Maurice M ben]

Also in this kind of problems you can use the Lagrangain concept, you don't need the Eulerian concept. but for the mass flow rate and so on you, need to use the principe of the conservation of mass.the continuity equation

 

[rwisz]

Great job on your attempt at solving this problem! Your approach using the kinematics equations is correct. To answer your question about the range, yes, you can use the same velocity but with the x-component. This is because the horizontal motion of the stream is unaffected by the vertical motion.

To find the range, you can use the equation x = v*t, where x is the range, v is the horizontal velocity, and t is the time. To find the time, you can use the equation y = vi*t + 1/2*a*t^2, where y is the vertical displacement (in this case, the height of the can), vi is the initial vertical velocity, and a is the acceleration due to gravity. Solving for t and substituting it into the first equation will give you the range.

Remember to convert your units to be consistent (i.e. convert meters to centimeters for the final answer). Keep up the good work!