How the water surface will be in a tilted glass

Hi, all. Do you think physics is difficult to understand. Then I must say this is the most enjoyable subject to discuss. Because physics is so common and part of us. Even including us, everything around us is governed by physics. It is the most fascinating subject. This world and even the entire universe is govern by physics. We will give and explain some illustrations of physics.

Why water in a glass always makes a horizontal surface even if the glass is tilted?

This question seems to be very obvious and even everyone has observed also. That, when we tilt a glass of water then, the water surface will not tilt with glass, but it always forms a horizontal surface.

To understand this phenomenon, we go by Newton’s Second Law of Motion. The sum of all forces acting on a body equals the change in its momentum, i.e F = dP/dt = d(m*v)/dt. When the water is in motion then the following forces will act on it.

F _total = F _gravity + F _viscous + F _Pressure

Where

F _gravity is the body force which will act due to the bulk and is equal to m*g.
F _viscous is the surface force which will act when the fluid is in motion and is given by F _viscous = – ƞ A dv/dx
F _Pressure is the surface force that acts due to the pressure gradient on the sides of the element under consideration.

Forces per unit Volume for all three forces acting on the fluid element can be written as :

f _total = f _gravity + f _viscous + f _pressure = m*g /V + f_viscous + (-P * A/V)
= ρg + f_viscous + (-∇ P) = ρ*a

In the present case of water inside the glass, the water is static. Hence, a= 0 & f _viscous = 0.

Therefore, ρg + (-∇ P) = 0
∇ P = ρg

In the above equation, the vector ∇P expresses the gradient of pressure, i.e the ∇P is perpendicular everywhere to the surface of constant pressure, P, which is equal to ρg. That means fluid in hydrostatic equilibrium will align its constant pressure surfaces everywhere normal to the local gravity vector.

Since the density of water in the glass is uniform everywhere, hence even if we tilt the glass, the surface which forms is always perpendicular to the direction of g, i.e downwards towards the earth.

Since, P = h*ρ*g , in the water of uniform density, at each and every height, h from the bottom of the glass, the pressure varies linearly with the height. At each height there will be a isobaric surface or surface of constant pressure. Or the water surface itself are isobaric surface, and hence they will always be perpendicular to the direction of g.

I Hope, with this explanation all of you will be able to appreciate the concept of pressure and how it affects the daily life experiences.