Flow of liquid through a hole and distance traveled

In summary, using the equations Q/pA = V, s=ut+1/2at^2, and v=d/t, the flow rate of a liquid from a 10mm hole in a storage tank holding 5m of liquid with a density of 490 kg/s is found to be 0.207 kg/s. With a resultant velocity of 5.45 m/s, the stream will travel 0.7824s and cover a horizontal distance of 4.26m before hitting the ground. It is uncertain if the dike located 1m away and 1m high will contain the flow, as the height of the hole and the mass flow rate and velocity of the stream may cause it to
  • #1
jcy128
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Homework Statement


if the flow rate of a liquid from a 10mm hole in a storage tank holding 5m of a liquid with a density of 490 kg/s, is 0.207 kg/s how far will this stream travel before it hits the ground and will it be contained by a dike 1 m away that is 1 m high

Homework Equations



Q=pAV => Q/pA = V
s=ut+1/2at^2
v=d/t

The Attempt at a Solution


so using the eqn Q/pA = V i get a resultant velocity of 5.45 m/s
using the vectors for the horizontal and vertical distances and the eqn s=ut+1/2at^2 I found that with this velocity the stream will travel for 0.7824s
and then using the eqn v=d/t and changing it to find distnace vt= d i found that the stream would travel 4.26m

I am uncertain how to calculate how to determine if the dike will contain the flow, I believe it won't due to the height of the hole and the mass flow rate and velocity of the stream
 
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  • #2
Welcome to PF!

Hi jcy128! Welcome to PF! :smile:

(try using the X2 tag just above the Reply box :wink:)

Your method is correct, but I don't get 5.45 for v, and you seem to have used 3m instead of 5m for t.

For the last part of the question, simply find how long it takes to fall to the level of the top of the dyke, and then see how far it has moved horizontally. :smile:
 

FAQ: Flow of liquid through a hole and distance traveled

What is the flow rate of liquid through a hole?

The flow rate of liquid through a hole depends on various factors such as the diameter of the hole, the pressure difference between the two sides of the hole, and the viscosity of the liquid. It can be calculated using the equation Q = A*v, where Q is the flow rate, A is the cross-sectional area of the hole, and v is the velocity of the liquid.

How does the diameter of the hole affect the flow of liquid?

The diameter of the hole directly affects the flow rate of liquid. A larger diameter hole will allow more liquid to pass through in a given time compared to a smaller diameter hole, assuming all other factors remain constant. This is because a larger hole has a greater cross-sectional area, allowing for more liquid to flow through.

What is the Bernoulli's principle and its relationship to the flow of liquid through a hole?

Bernoulli's principle states that as the speed of a fluid increases, the pressure decreases. This principle is applicable to the flow of liquid through a hole, as the velocity of the liquid will increase as it passes through a smaller hole, causing a decrease in pressure. This decrease in pressure can result in a higher flow rate of liquid.

How can the distance traveled by liquid through a hole be calculated?

The distance traveled by liquid through a hole can be calculated using the equation d = (v^2 * t)/2, where d is the distance traveled, v is the velocity of the liquid, and t is the time taken. This equation assumes that the liquid is flowing through a horizontal hole and there is no external force acting on the liquid.

What are some practical applications of studying the flow of liquid through a hole?

The study of flow of liquid through a hole has various practical applications in fields such as engineering, physics, and hydrology. It can be used to design efficient plumbing systems, optimize the flow of liquids in industrial processes, and understand the movement of groundwater through porous materials. It is also essential in the design of pumps and other fluid handling equipment.

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