--- title: "Specific gravity, weight and Newtonian fluids" subject: "Hydro Power" chapter: 1 key: "semester_6/hydro_power:newtonian-non-newtonian-fluids" source: https://www.bctengineer.com/q/semester_6/hydro_power/newtonian-non-newtonian-fluids site: BCT Engineering --- # Specific gravity, weight and Newtonian fluids Hydro Power · Chapter 1: Introduction to Basic Fluid Mechanics and Hydraulics - Asked in: 2070 Bhadra, 2+4 marks - Video: [Fluid Properties: Density, Specific Weight, and Specific Gravity](https://www.youtube.com/watch?v=IIj2eOr2gAc) — HydroMohsen - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/hydro_power/newtonian-non-newtonian-fluids - Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-1 ## Question Define the terms specific gravity and specific weight. Differentiate between Newtonian and Non-Newtonian fluid showing diagram of variations of shear stress with velocity gradient. ## Short answer Specific weight is weight per unit volume (γ = ρg). Specific gravity is density ratio to water. Newtonian fluids obey τ = μ du/dy with constant viscosity, giving a straight line through origin. Non-Newtonian fluids deviate, with viscosity changing with shear rate, producing curved or offset graphs. ## Answer #### 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 $\tau = A\left(\frac{du}{dy}\right)^n + B$. ```text 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) ``` | Point | Newtonian | Non-Newtonian | |---|---|---| | Law | $\tau = \mu\, du/dy$ | $\tau = A(du/dy)^n + B$ | | $\tau$ vs $du/dy$ graph | Straight line through origin | Curve, or line not through origin | | Viscosity | Constant at given temperature | Changes with shear rate | | Yield stress | None | May exist (Bingham plastic) | | Examples | Water, air, kerosene, petrol | Blood, paint, toothpaste, sewage sludge, cement slurry | 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). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. A Newtonian fluid is one in which: A. Shear stress is proportional to velocity gradient with constant viscosity B. Viscosity changes with shear rate C. A yield stress must be exceeded before flow D. Shear stress is independent of velocity gradient Answer: A. Newtonian fluids obey tau = mu du/dy; the tau vs du/dy graph is a straight line through the origin. (Key point: Newtonian fluid) 2. Which fluid needs a yield stress before it flows? A. Water B. Air C. Bingham plastic such as toothpaste D. Kerosene Answer: C. A Bingham plastic flows only after the yield stress is exceeded and then behaves linearly. (Key point: Bingham plastic) 3. In tau = A(du/dy)^n + B, which is correct? A. Pseudo-plastic n < 1, dilatant n > 1 B. Pseudo-plastic n > 1, dilatant n < 1 C. Both have n = 1 D. Pseudo-plastic n = 0, dilatant n = 2 Answer: A. Pseudo-plastic (paint, blood) has slope decreasing, n < 1; dilatant (quicksand) has slope increasing, n > 1. (Key point: Pseudo-plastic vs dilatant) 4. Specific gravity of a liquid is: A. Its weight per unit volume in N/m^3 B. Ratio of its density to that of water at 4 C, with no unit C. Its volume per unit mass D. Its viscosity divided by density Answer: B. S = rho/rho_w is dimensionless; mercury has S = 13.6. (Key point: Specific gravity) ## Related in Hydro Power - [Definitions of basic fluid properties](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Afluid-property-definitions) — Hydro Power, chapter 1, asked 3× - [Stresses in gravity dam with drain holes](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Agravity-dam-stresses-figure) — Hydro Power, chapter 4 - [Stability of gravity dam (crest 1530 m)](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Agravity-dam-stability-1530) — Hydro Power, chapter 4 - [Elementary profile and 40 m gravity dam stability](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Agravity-dam-elementary-40m) — Hydro Power, chapter 4 - [Triangular gravity dam 35 m high](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Atriangular-dam-35m) — Hydro Power, chapter 4 - [Sliding and overturning check of gravity dam](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Agravity-dam-sliding-overturning-figure) — Hydro Power, chapter 4 ## Related in other subjects - [Newtonian or non-Newtonian fluid from data](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Anewtonian-or-not-table) — Fluid Mechanics, chapter 1 - [Gravity dam section: shear stress near toe (2082)](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Agravity-dam-stability-2082-baishakh) — Hydropower Engineering, chapter 4 - [Gravity dam stability and shear stress at toe (2081)](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Agravity-dam-stability-2081-bhadra) — Hydropower Engineering, chapter 4 - [Navier-Stokes equations for Newtonian fluid](https://www.bctengineer.com/question.md?key=semester_4%2Ffluid_mechanics_mechanical%3Anavier-stokes-newtonian-fluid) — Fluid Mechanics, chapter 4