Why does water get 'hard' on impact?

[Ask1122]

Hi all, have been wondering, why is it that when you put your hand in water, it's soft and there is hardly any resistance, but when you jump into it like from 100m above, you will most probably kill yourself?

Is it because there is not enough time for the forces to distribute across the water molecules at the time of impact?

 

[HallsofIvy]

How much resistance force (friction force) an object moving through a medium experiences depends upon the speed (obviously- no speed, no force!) and experimentation has shown that the resistance to motion in water is roughly proportional to the speed cubed. That is, if you go through water at twice the speed, you feel eight times the force.

 

[tuoni]

It is due to drag, the resistance to a body traveling through a fluid.

F_{drag} = \frac{k_{drag}\rho v^{2}A}{2}

k_drag — drag constant (k/1)
ρ — mass density of medium (kg/m^3)
v — velocity relative to medium (m/s)
A — cross-sectional normal area (m^2)

Let's say that water has a mass density of 1000 kg/m^3, the impact velocity is 20 m/s, the normal area at impact (of two feet) is ~0.03 m^2, and the drag constant is 0.9. This results in an instantaneous force of 5.4 kN.

 

[Ask1122]

Thanks for the reply guys!
I suppose that drag equation are used in drag for cars as well?

 

[mgb_phys]

I suppose that drag equation are used in drag for cars as well?

Yes, that's the drag equation for cars ( k is normally written as Cd for aerodynamic drag)

The drag equation not really correct for hitting the surface of water, the equation is valid for what we call turbulent flow - when you are going fast through a fluid and the air or water is swirling past you. There is a different equation for when you are going slowly through a thicker fluid - like oil flowing through an engine

Notice that it depends on Cd (which is why makers quote it for sports cars) - how streamlined the shape is.
but also A (the front area) - which is why fast cars are small.
And V^2, so as you go twice as fast the drag increases by 4 times - this is what really limits the speed of cars.

 

[salb4]

it's called surface tension