Specific gravity, weight and Newtonian fluids

Specific gravity and specific weight

• Specific weight ($\gamma$ or $w$): weight per unit volume of a fluid, $\gamma = \rho g$ (N/m³). For water $\gamma = 9810$ N/m³.
• Specific gravity ($S$): ratio of the specific weight (or density) of a fluid to that of a standard fluid (water at 4 °C for liquids). $S = \gamma/\gamma_w$; it has no unit. For mercury $S = 13.6$.

Newtonian and non-Newtonian fluids

A Newtonian fluid obeys Newton's law of viscosity: shear stress is directly proportional to velocity gradient, with a constant viscosity:

$$\tau = \mu \frac{du}{dy}$$

A non-Newtonian fluid does not obey this linear law; its apparent viscosity changes with the rate of shear, in general $\tau = A\left(\frac{du}{dy}\right)^n + B$.

 tau ^          B
     |         /        P
     |        /     _.-'
     |       /   .-'      N
     |      /  .'      .-'
     |     / .'     .-'
  ty +----'.'    .-'       D
     |   .'   .-'      _.-'
     |  /  .-'    _.--'
     | / .-' _.--'
     |/.-_.-'
     +--------------------> du/dy
 N = Newtonian (straight line from 0)
 P = pseudo-plastic (slope decreases)
 D = dilatant (slope increases)
 B = Bingham plastic (flows only after
     yield stress ty, then linear)

Types of non-Newtonian fluids: pseudo-plastic ($n<1$, e.g. paint, blood), dilatant ($n>1$, e.g. rice starch, quicksand), Bingham plastic (needs a yield stress before flowing, e.g. toothpaste, sewage sludge).