Physics · Mechanical Properties Of Fluids · NEET
No. Velocity gradient is how much the layer speed changes per unit distance across the flow, not the speed itself. In laminar flow the top layer may move at v while the bottom layer is at rest, and the change happens over a gap x. The velocity gradient is dv/dx (change in velocity divided by the distance across the layers). Its SI unit is (m/s) per m = per second (s^-1). A big velocity gradient means neighbouring layers slip past each other quickly.
Newton found that the viscous (drag) force between two liquid layers is directly proportional to the area of contact A and to the velocity gradient dv/dx. So F is proportional to A times (dv/dx). Putting a constant, F = eta A (dv/dx). Here eta (eta, the Greek letter) is the coefficient of viscosity of the liquid. The minus sign is sometimes added to show the force opposes relative motion: F = -eta A (dv/dx).
Because layers stick to each other. A faster layer tries to drag the slower layer forward, and the slower layer drags the faster one backward. So on the fast-moving layer the viscous force acts backward, slowing it down, just like friction. This is why NCERT calls viscosity an internal friction between liquid layers. It only appears when there is relative motion between layers.
Yes. From F = eta A (dv/dx), doubling the contact area A doubles the viscous force (if the velocity gradient stays the same). This is different from Stokes' law (F = 6 pi eta r v) which is for a sphere. For flat sliding layers or a plate on a liquid film, always use F = eta A (dv/dx).
They are the same idea. NCERT says that in a fluid the stress depends on the rate of change of strain (strain rate) which equals v/l, the velocity gradient. So eta = shearing stress divided by strain rate = (F/A) / (v/l). Rearranging gives F = eta A v / l, the same as Newton's law with dv/dx replaced by v/l for a uniform gradient.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Per second (s^-1). It comes from dividing velocity (m/s) by distance (m), which gives 1/s.
F = eta A (dv/dx), where eta is the coefficient of viscosity, A is the area of the layers in contact, and dv/dx is the velocity gradient.
No. Viscosity (coefficient eta) is a fixed property of the liquid. Viscous force is the actual drag force in newtons, and it depends on eta, the area, and the velocity gradient.
When there is no relative motion between layers, that is when the velocity gradient dv/dx is zero. If all layers move at the same speed (or the liquid is at rest), no viscous force acts.
Because it resists relative motion between liquid layers, just like friction resists a solid sliding on a surface. Faster layers are pulled back and slower layers are pulled forward.
