Question

A large water tank, open at the top, has a small hole in the bottom. When
the water level is 5 m above the bottom of the tank, the speed of the water leaking from
the hole: (Use ! = 10 N/kg.) [Hint: Use Bernoulli

Answer 1

Let
p1 = pressure just above orifice (in water)
p2 = pressure just below orifice (in air)
rho = density of water, unchanged above & below orifice
v1 = velocity of water just above orifice, in tank = 0
v2 = velocity of water just below orifice, in air
h1-h2 = orifice thickness, assumed zero:

Bernoulli: p+ (1/2)*rho*v^2 + rho*g*y = constant. But since top & bottom of orifice are assumed at same height, h2 = h1 so this simplifies to

p1 - p2 = (rho/2)*(v2^2 - v1^2) with

V = ?2gh = ?(2)(9.8)(5) = ?98 =9.89 m/s