/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 62 A shaft with outside diameter of... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 62

A shaft with outside diameter of \(18 \mathrm{mm}\) turns at 20 revolutions per second inside a stationary journal bearing \(60 \mathrm{mm}\) long. A thin film of oil \(0.2 \mathrm{mm}\) thick fills the concentric annulus between the shaft and journal. The torque needed to turn the shaft is \(0.0036 \mathrm{N} \cdot \mathrm{m}\). Estimate the viscosity of the oil that fills the gap.

Short Answer

Expert verified
The viscosity of the oil is calculated as \(0.0845 Ns/m^2\) or \(0.0845 Pas\).

Step by step solution

01

List Given Information

The outside diameter of the shaft, the length of the journal bearing, the thickness of the oil, and the torque needed to turn the shaft are given, respectively as: 18mm, 60mm, 0.2mm and 0.0036 N路m. Also the shaft turns at 20 revolutions per second which is converted to angular velocity as \(2\pi n = 2\pi x 20 = 40\pi rad/sec\).
02

Convert Units

First, convert the units of the given quantities to SI units. The length L, the radius R of shaft and thickness of oil in meters are: \(L = 60mm = 60/1000 m = 0.06m\), \(R = \frac{18mm}{2} = 9mm = 9/1000 m = 0.009m\), \(t = 0.2mm = 0.2/1000 m = 0.0002m\).
03

Apply the Formula for Torque

Now apply the formula for torque on a rotating cylinder \(T=2\pi L\eta R^{2}n\). Solving this equation for viscosity \(\eta\), we get \(\eta=\frac{T}{2\pi L R^{2}n}\).
04

Substitute the Given Values

Substitute the given values into the formula: \(\eta=\frac{0.0036}{2\pi*0.06*0.009^{2}*40\pi}\) .
05

Calculate the Viscosity

Calculate the expression above to find the numerical value of the viscosity \(\eta\) of the oil.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A flow is described by velocity field \(\vec{V}=a x \hat{i}+b \hat{j},\) where \(a=1 / 5 \mathrm{s}^{-1}\) and \(b=1 \mathrm{m} / \mathrm{s}\). Coordinates are measured in meters. Obtain the equation for the streamline passing through point \((1,1) .\) At \(t=5 \mathrm{s}\), what are the coordinates of the particle that initially (at \(t=0\) ) passed through point (1,1)\(?\) What are its coordinates at \(t=10\) s? Plot the streamline and the initial, \(5 \mathrm{s}\), and 10 s positions of the particle. What conclusions can you draw about the pathline, streamline, and streakline for this flow?

The thin outer cylinder (mass \(m_{2}\) and radius \(R\) ) of a small portable concentric cylinder viscometer is driven by a falling mass, \(m_{1},\) attached to a cord. The inner cylinder is stationary. The clearance between the cylinders is \(a\). Neglect bearing friction, air resistance, and the mass of liquid in the viscometer. Obtain an algebraic expression for the torque due to viscous shear that acts on the cylinder at angular speed \(\omega\) Derive and solve a differential equation for the angular speed of the outer cylinder as a function of time. Obtain an expression for the maximum angular speed of the cylinder.

The velocity field \(\vec{V}=A x \hat{i}-A y \tilde{j},\) where \(A=2 s^{-1},\) can be interpreted to represent flow in a corner. Find an equation for the flow streamlines. Explain the relevance of \(A .\) Plot several streamlines in the first quadrant, including the one that passes through the point \((x, y)=(0,0)\).

Streaklines are traced out by neutrally buoyant marker fluid injected into a flow ficld from a fixed point in space. A particle of the marker fluid that is at point \((x, y)\) at time \(t\) must have passed through the injection point \(\left(x_{0}, y_{0}\right)\) at some earlier instant \(t=\tau .\) The time history of a marker particle may be found by solving the pathline equations for the initial conditions that \(x=x_{0}, y=y_{0}\) when \(t=\tau .\) The present locations of particles on the streakline are obtained by setting \(\tau\) equal to values in the range \(0 \leq \tau \leq t\). Consider the flow ficld \(\vec{V}=a x(1+b t) \hat{i}+c y \hat{j},\) where \(a=c=1 \mathrm{s}^{-1}\) and \(b=0.2 \mathrm{s}^{-1}\). Coordinates are measured in meters. Plot the streakline that passes through the initial point \(\left(x_{0}, y_{0}\right)=(1,1),\) during the interval from \(t=0\) to \(t=3\) s. Compare with the streamline plotted through the same point at the instants \(t=0,1,\) and \(2 \mathrm{s}\).

A viscous liquid is sheared between two parallel disks; the upper disk rotates and the lower one is fixed. The velocity field between the disks is given by \(\vec{V}=\hat{e}_{0} r \omega z / h\). (The origin of coordinates is located at the center of the lower disk; the upper disk is located at \(z=h .\) ) What are the dimensions of this velocity field? Does this velocity field satisfy appropriate physical boundary conditions? What are they?
See all solutions

Recommended explanations on Physics Textbooks

Magnetism

Read Explanation

Quantum Physics

Read Explanation

Circular Motion and Gravitation

Read Explanation

Oscillations

Read Explanation

Work Energy and Power

Read Explanation

Wave Optics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.