Physics · Mechanical Properties Of Fluids · NEET
Pa·s is the SI unit. It is also called the poiseuille (Pl) and can be written as N·s/m^2. Poise is the CGS unit, NOT the SI unit. Many students wrongly tick poise as SI in exams. Conversion: 1 Pa·s = 10 poise, so 1 poise = 0.1 Pa·s. Water at room temperature has viscosity about 0.001 Pa·s = 0.01 poise = 1 centipoise.
Start from Newton's formula F = eta * A * (dv/dx). So eta = F / (A * velocity gradient). Force F has dimension [M L T^-2]. Area A has [L^2]. Velocity gradient (dv/dx) is (m/s)/m = 1/s, dimension [T^-1]. So eta = [M L T^-2] / ([L^2] * [T^-1]) = [M L T^-2] / [L^2 T^-1] = [M L^-1 T^-1]. Cancel carefully: L power = 1 - 2 = -1, T power = -2 - (-1) = -1.
eta = shearing stress / strain rate. Shearing stress is a pressure, unit Pa. Strain rate (velocity gradient) has unit per second, s^-1. Dividing Pa by s^-1 is the same as multiplying by s, giving Pa·s. So viscosity is pressure multiplied by time. That extra 'time' factor is what separates viscosity from a plain pressure.
No. Pressure and stress have dimension [M L^-1 T^-2]. Viscosity has [M L^-1 T^-1], which has one less power of time (T^-1 instead of T^-2). So they are close but not equal. A quick check: viscosity = pressure * time, so its dimension = [M L^-1 T^-2] * [T] = [M L^-1 T^-1].
1 poise = 1 g/(cm·s). Convert: 1 g = 10^-3 kg, 1 cm = 10^-2 m. So 1 poise = 10^-3 kg / (10^-2 m * 1 s) = 10^-3 / 10^-2 = 10^-1 kg/(m·s) = 0.1 Pa·s. Therefore 1 Pa·s = 10 poise. Remember the factor 10, not 100.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Pa·s (pascal second), also called poiseuille (Pl) or N·s/m^2.
Poise, defined as 1 g/(cm·s). 1 Pa·s = 10 poise.
[M L^-1 T^-1], derived from eta = force / (area * velocity gradient).
1 Pa·s = 10 poise, and 1 poise = 0.1 Pa·s.
No. Pressure is [M L^-1 T^-2]; viscosity is [M L^-1 T^-1]. Viscosity = pressure * time.
