---
title: "Viscosity of oil on inclined plane"
subject: "Hydro Power"
chapter: 1
key: "semester_6/hydro_power:viscosity-inclined-plane"
source: https://www.bctengineer.com/q/semester_6/hydro_power/viscosity-inclined-plane
site: BCT Engineering
---

# Viscosity of oil on inclined plane

Hydro Power · Chapter 1: Introduction to Basic Fluid Mechanics and Hydraulics

- Asked in: 2077 Chaitra, 7 marks
- Video: [Fluid Mechanics 1.4 - Viscosity Problem with Solution - Terminal Velocity on Inclined Plate](https://www.youtube.com/watch?v=0Y3VvPiF7hg) — Rasim Guldiken
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/hydro_power/viscosity-inclined-plane
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-1

## Question

Calculate the dynamic viscosity of oil which is used for the lubrication between square plate of size 0.8 m × 0.8 m and an inclined plane with an angle of inclination 30°. The weight of the square plate is 300 N and it slides down the inclined plane with a uniform velocity of 0.3 m/s. The thickness of oil film is 1.5 mm.

## Short answer

Downslope force F = 300 sin30° = 150 N, shear stress τ = 150/0.64 = 234.375 Pa, gradient du/dy = 0.3/0.0015 = 200 s⁻¹. Dynamic viscosity μ = τ/(du/dy) = 1.172 N·s/m².

## Answer

The plate slides at uniform velocity, so the component of its weight along the plane is balanced by the viscous shear force of the oil film.

**Given:** $A = 0.8 \times 0.8 = 0.64$ m², $W = 300$ N, $\theta = 30^\circ$, $u = 0.3$ m/s, $t = 1.5$ mm $= 0.0015$ m.

```text
          plate (W = 300 N)
         _/_/
        /  /  ---> slides down at 0.3 m/s
       /  / oil film 1.5 mm
      /__/________
     /  30 deg
```

#### Shear force and shear stress
$$
\begin{aligned}
F &= W \sin 30^\circ = 300 \times 0.5 = 150\ \text{N} \\
\tau &= \frac{F}{A} = \frac{150}{0.64} = 234.375\ \text{N/m}^2
\end{aligned}
$$

#### Velocity gradient (linear profile)
$$
\frac{du}{dy} = \frac{0.3}{0.0015} = 200\ \text{s}^{-1}
$$

#### Viscosity
$$
\mu = \frac{\tau}{du/dy} = \frac{234.375}{200} = 1.172\ \text{N·s/m}^2
$$

**Answer:** dynamic viscosity of the oil $\mu = 1.172$ N·s/m² (= 11.72 poise).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. The plate slides at uniform velocity, so the viscous shear force equals:
   A. The full weight W
   B. W cos 30 degrees
   C. W sin 30 degrees
   D. Zero
   Answer: C. At uniform velocity the weight component along the plane, W sin 30 = 150 N, balances the shear force. (Key point: Force balance)

2. The shear stress on the 0.8 m x 0.8 m plate is:
   A. 234.4 N/m^2
   B. 468.8 N/m^2
   C. 187.5 N/m^2
   D. 300 N/m^2
   Answer: A. tau = 150/0.64 = 234.375 N/m^2. (Key point: Shear stress)

3. For velocity 0.3 m/s and film thickness 1.5 mm, du/dy is:
   A. 0.2 s^-1
   B. 20 s^-1
   C. 200 s^-1
   D. 450 s^-1
   Answer: C. du/dy = 0.3/0.0015 = 200 s^-1. (Key point: Velocity gradient)

4. The dynamic viscosity of the oil is about:
   A. 0.85 N.s/m^2
   B. 1.172 N.s/m^2
   C. 2.34 N.s/m^2
   D. 46.9 N.s/m^2
   Answer: B. mu = 234.375/200 = 1.172 N.s/m^2 (11.72 poise). (Key point: Viscosity result)

## Related in Hydro Power

- [Viscosity of oil between parallel plates](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Aviscosity-parallel-plates) — Hydro Power, chapter 1
- [Pressure on inclined rectangular plate](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Ainclined-rectangular-plate) — Hydro Power, chapter 1
- [Penstock plate thickness (1.5 m, 250 m head)](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Apenstock-thickness-1-5m) — Hydro Power, chapter 5
- [Specific gravity, weight and Newtonian fluids](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Anewtonian-non-newtonian-fluids) — Hydro Power, chapter 1

## Related in other subjects

- [Plate sliding on inclined oil film](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Aincline-plate-oil-viscosity) — Fluid Mechanics, chapter 1
- [Hydrodynamic lubrication theory and film formation](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Ahydrodynamic-lubrication-theory) — Machine Design I, chapter 7
- [Journal bearing design with film thickness check](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Ajournal-bearing-minimum-film-thickness) — Machine Design I, chapter 7
- [Viscosity of oil from laminar pipe flow](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Ahorizontal-oil-pipe-laminar-viscosity) — Hydraulics, chapter 1