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

# Viscosity of oil between parallel plates

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

- Asked in: 2081 Chaitra, 5 marks
- Video: [Viscosity of Fluids & Velocity Gradient - Fluid Mechanics, Physics Problems](https://www.youtube.com/watch?v=PoG14wRRQmM) — The Organic Chemistry Tutor
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/hydro_power/viscosity-parallel-plates
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-1

## Question

The space between two parallel plates, 5 mm apart, is filled with crude oil. A force of 2 N is required to drag the upper plate at a constant velocity of 0.8 m/s, while the lower plate remains stationary. The area of the upper plate is 0.09 m². Determine the dynamic viscosity and kinematic viscosity of the oil, given that the specific gravity of the oil is 0.9.

## Short answer

Shear stress τ = F/A = 22.22 Pa, velocity gradient du/dy = 0.8/0.005 = 160 s⁻¹. Dynamic viscosity μ = τ/(du/dy) = 0.1389 N·s/m². Density ρ = 0.9×1000 = 900 kg/m³, kinematic viscosity ν = μ/ρ = 1.543×10⁻⁴ m²/s.

## Answer

Use Newton's law of viscosity, $\tau = \mu\, du/dy$, with a linear velocity distribution between the plates.

**Given:** gap $dy = 5$ mm $= 0.005$ m, $F = 2$ N, $u = 0.8$ m/s, $A = 0.09$ m², $S = 0.9$.

#### Dynamic viscosity
$$
\begin{aligned}
\tau &= \frac{F}{A} = \frac{2}{0.09} = 22.22\ \text{N/m}^2 \\
\frac{du}{dy} &= \frac{0.8 - 0}{0.005} = 160\ \text{s}^{-1} \\
\mu &= \frac{\tau}{du/dy} = \frac{22.22}{160} = 0.1389\ \text{N·s/m}^2
\end{aligned}
$$

#### Kinematic viscosity
$$
\begin{aligned}
\rho &= 0.9 \times 1000 = 900\ \text{kg/m}^3 \\
\nu &= \frac{\mu}{\rho} = \frac{0.1389}{900} = 1.543 \times 10^{-4}\ \text{m}^2/\text{s}
\end{aligned}
$$

**Answer:** $\mu = 0.1389$ N·s/m² (= 1.389 poise), $\nu = 1.543 \times 10^{-4}$ m²/s (= 1.543 stokes).

## Check yourself

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

1. For F = 2 N on a plate of area 0.09 m^2, the shear stress is about:
   A. 0.18 N/m^2
   B. 22.2 N/m^2
   C. 160 N/m^2
   D. 0.045 N/m^2
   Answer: B. tau = F/A = 2/0.09 = 22.22 N/m^2. (Key point: Shear stress)

2. With a linear profile, 0.8 m/s over a 5 mm gap gives du/dy of:
   A. 0.16 s^-1
   B. 4 s^-1
   C. 160 s^-1
   D. 1600 s^-1
   Answer: C. du/dy = 0.8/0.005 = 160 s^-1 (gap must be in metres). (Key point: Velocity gradient)

3. The dynamic viscosity of the oil is:
   A. 0.1389 N.s/m^2
   B. 1.389 N.s/m^2
   C. 7.2 N.s/m^2
   D. 0.0139 N.s/m^2
   Answer: A. mu = tau/(du/dy) = 22.22/160 = 0.1389 N.s/m^2. (Key point: Dynamic viscosity)

4. With S = 0.9, kinematic viscosity is nu = mu/rho where rho is:
   A. 0.9 kg/m^3
   B. 900 kg/m^3
   C. 9810 kg/m^3
   D. 1000 kg/m^3
   Answer: B. rho = 0.9 x 1000 = 900 kg/m^3, so nu = 0.1389/900 = 1.543e-4 m^2/s. (Key point: Kinematic viscosity)

## Related in Hydro Power

- [Viscosity of oil on inclined plane](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Aviscosity-inclined-plane) — Hydro Power, chapter 1
- [Manometer between oil and water pipes](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Amanometer-oil-water-pipes) — Hydro Power, chapter 1
- [Pressure on rectangular plate 3 m × 5 m](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Arectangular-plate-3x5) — 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
- [Pressure on isosceles triangular plate](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Atriangular-plate-pressure) — 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

## Related in other subjects

- [Plate towed between two parallel walls](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Aplate-between-walls-force) — Fluid Mechanics, chapter 1
- [Force of jet on flat plate, stationary and moving](https://www.bctengineer.com/question.md?key=semester_5%2Ffluid_machines%3Ajet-on-flat-plate-numerical) — Fluid Machines, chapter 1
- [Oil flow between fixed plates problem](https://www.bctengineer.com/question.md?key=semester_4%2Ffluid_mechanics_mechanical%3Aoil-flow-between-plates-numerical) — Fluid Mechanics, chapter 6
- [Is flow between parallel plates rotational?](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Aparallel-plates-rotational-check) — Fluid Mechanics, chapter 4