Calculating Stream Impact Distance from Container with Bernouilli's Equation

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Homework Help Overview

The discussion revolves around calculating the distance from a container to the point where a stream of water impacts the floor, using Bernoulli's Equation and principles of projectile motion. The problem involves understanding fluid dynamics and kinematics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss using Bernoulli's Equation to find the velocity of the fluid exiting the container and then applying projectile motion to determine the impact distance. Questions arise regarding the necessary parameters, such as the height of the hole and the initial velocity.

Discussion Status

Participants are actively exploring the relationship between fluid velocity and projectile motion. Some have provided guidance on using kinematic equations once the velocity is determined, while others confirm the approach without reaching a consensus on the final calculations.

Contextual Notes

There is an emphasis on the need for specific measurements, such as the height of the hole and the time of flight, which are not fully detailed in the discussion. Participants are also navigating the assumptions inherent in applying Bernoulli's principles and kinematic equations.

CollectiveRocker
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If I have a container, filled with water, and a hole is cut in the side at some distance h from the top, how do I go about finding the distance R from the foot of the container that the stream will impact the floor? Do I use Bernouilli's Equation: P1 + ½ pv12 + pgy1 = P2 + ½ pv22 + pgy2 Where P = pressure at depth h, p = density of fluid, and y1 & y2 are = two heights about surface. Or is there another way?
 
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1.By Benoulli, you find the velocity by which the fluid leaves the container (Torricellis law).
2. Use projectile motion to determine R (you'll need to know how high above the ground the hole is)
 
If v = (2gh)^1/2, then we turn to use the kinematic equations. y = H(height from top water level to floor)-h(height of top water level to hole in side of container), we know g, all we're missing is the original velocity, time, and acceleration. Is there something I'm missing?
 
Your not missing anything. If you have the velocity, the rest is just simple kinematics.
 
I get R = ((2gh)^(1/2))*t, is this correct?
 
As long as "t" is the time it takes to reach the ground, yes.
 

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