Fluid/Stream Que work shown need guidance

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Homework Help Overview

The problem involves a can filled with water, where a hole at a specific height produces a stream directed at an angle. Participants are tasked with finding the range and maximum height of the stream based on the given parameters.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to calculate the initial velocity of the stream and its vertical component, expressing confusion about the range calculation using the horizontal component. Other participants provide corrections and suggest using kinematic equations for further calculations.

Discussion Status

Participants are actively engaging with the problem, offering guidance on maintaining significant figures and correcting minor errors in calculations. There is a mix of interpretations regarding the application of different concepts, such as Lagrangian and Eulerian approaches, as well as the continuity equation.

Contextual Notes

There is mention of significant figures and the importance of maintaining them throughout calculations. The discussion also highlights potential confusion regarding the use of different components of velocity and the application of kinematic equations.

jen333
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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!
 
Last edited:
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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.
 
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
 
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