speed of water?

Question

a small crack occures at the base of a 15.0 m high dam. the effective crack area through which water leaves is 1.30 X 10^-3m^2. ignoring viscous losses, what is the speed of water flowing throught the crack?

Answer 1

applying bernouli equation between the water at the surface of dam and water at 15m deep which is going out of crack;

►P1/γ1 + V1^2/2g + z1 = P2/γ2 + V2^2/2g + z2

P1=P2
z1-z2=15m
V1=0

=>
V2^2/2g = z1-z2 => ►V2= Sqrt(2g(z1-z2))

v2= Sqrt(2*9.8*15) = 17.15 m/s◄

Note: the effect of area is on volumetric flow rate;

Hope this helps

Answer 2

v = √(15 m)(9.8 m/s^2) = 12.124 m/s