Water flowing through an eavestrough

1. The problem statement, all variables and given/known data

6. During a storm, water flows off a roof into an eaves trough and then down from a 5.0 cm diameter hole in the bottom of it. The water in the trough is 2.5 cm deep. (Torricelli’s law & Bernoulli’s equation )

a. What is the speed (velocity) of the flow as it leaves the bottom of the trough?

b. What is the speed of the flow just before it hits the ground, 4.0 m below the hole?

c. What is the diameter of the flow there?

d. What is the volumetric and mass flow rate?

2. Relevant equations

Equation 1
[tex]v = \sqrt{2gh}[/tex]

Equation 2
[tex]P_1 + \frac{1}{2}\rho v_1^2 + \rho g h_1 = P_2 + \frac{1}{2} \rho v_2^2 + \rho g h_2[/tex]

3. The attempt at a solution

Parts A and B seem simple enough, just use equation 1 (would h for part B be 4.025m), but I’m not sure how Bernoulli’s equation comes into play. There is the continuity equation A1V1 = A2V2 that relates diameter and velocity, but the question states that this is a Torricelli’s law & Bernoulli’s equation problem. Do I maybe sub that equation into Bernoulli’s equation? Part D seems like it follows pretty easily from the others so I don’t really need help on that, but the others have me confused.

Any help is appreciated, thanks!


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