The Victoria Falls in ZambiaZimbabwe are approximately 108 m

The Victoria Falls in Zambia/Zimbabwe are approximately 108 m (360 ft) high. If the water flows over the crest of the falls with a velocity of 2.4 m/s, and viscous effects are neglected, with what velocity does the water strike the rocks at the bottom of the falls? Estimate the maximum pressure of the water on these rocks. Comment upon whether or not it is reasonable to neglect viscous effects for this flow.

Solution

let area of the mouth of the river be A, velocity at mouth be u
for time dt, dm water flows off the cliff
dm = (rho) dV = (rho) A dx = (rho) A u dt

now g h (dm) + 0.5 u ^2 * (dm) = 0.5 * v ^2 * (dm)
v = sqroot(2gh + u^2) = sqroot(2*9.8*108 + 2.4^2) = 46.07 m/s

let this dm have df force on the rocks

df = v * dm / dt = v * (rho) A u
pressure = v (rho) u = 46.07 *1000 * 2.4 = 110.570 kPa

Visous effects should not be ignored as a lot of energy is lost due to that which would change the expression for final velocity and hence the pressure, but for very large hieght these might be very less