Determine the speed at which the water leaves the hole

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SUMMARY

The discussion focuses on calculating the speed at which water exits a hole in a storage tank and determining the diameter of that hole. The flow rate is given as 2.10x10-3 m3/min, leading to a calculated exit speed of 17.15 m/s. The participants suggest using the volumetric flow rate equation Q = Av and apply Bernoulli's principle to relate pressure energy and kinetic energy for the calculations. The area of the hole can be derived from the flow rate and exit speed.

PREREQUISITES
  • Understanding of fluid dynamics principles, specifically Bernoulli's equation.
  • Familiarity with volumetric flow rate calculations (Q = Av).
  • Basic knowledge of area and diameter calculations in geometry.
  • Concept of conservation of energy in fluid systems.
NEXT STEPS
  • Study Bernoulli's equation and its applications in fluid dynamics.
  • Learn how to derive the area from volumetric flow rate and velocity.
  • Explore the relationship between flow rate, area, and diameter in fluid mechanics.
  • Investigate real-world applications of fluid flow through orifices and holes.
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Students in physics or engineering, particularly those studying fluid dynamics, as well as professionals involved in hydraulic systems and water management.

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Homework Statement



A large storage tank, open to the atmosphere at the top and filled with water, develops a small hole in its side at a point 15.0 m below the water level. If the rate of flow from the leak is 2.10x10-3 m3/min

(a) Determine the speed at which the water leaves the hole. =17.15m/s


(b) Determine the diameter of the hole. = ?


Homework Equations



F=eta(Av/d)

I'm not sure what equation to use for this.

The Attempt at a Solution



I'm just not sure how to start this.
Any suggestions?
 
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The volumeteric flow rate is given by Q = Av.

You are given Q and you have apparently found v (the velocity), so just solve for A (the area) and then calculate the diameter.
 
a) Conservation of energy. The pressure energy of the water just inside the hole is equal to the kinetic energy of the water just outside the hole. See Bernoulli for terms in the equation.

b) I think it is acceptable (= a good approximation) to assume constant velocity across the whole are of the whole so stewartcs' formula applies.
 

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