Determine the speed at which the water leaves the hole

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The discussion focuses on calculating the speed at which water exits a hole in a storage tank and determining the hole's diameter. The speed of the water leaving the hole is calculated to be 17.15 m/s based on the volumetric flow rate provided. Participants suggest using the equation Q = Av to find the area of the hole, which can then be used to calculate the diameter. The conservation of energy principle and Bernoulli's equation are referenced as foundational concepts for these calculations. The conversation emphasizes the importance of understanding fluid dynamics in solving the problem effectively.
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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.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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