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1.2. moving plate U plate = Umax Ufluid =0 u (velocity) A U fluid =Umax stationary plate F T j Viscosity: A shearing force of F = 10 dynes is applied to a rectangular plate of 5 x 10 cm dimensions, which sits on top of an h = 0.5 mm high column of Newtonian fluid that is initially at rest. As a result of the shearing force, the plate moves at a speed of u = 1 cm/s. (Note that 1 dyne = 1 g cm s².) a. What is the viscosity of this Newtonian fluid? b. What shearing force F would be required if the fluid column height h were doubled? c. What shearing force F would be required if the fluid column height h were halved? d. Plot the viscosity on the provided rate of shear vs. shear stress graph.

1.2. moving plate U plate = Umax Ufluid =0 u (velocity) A U fluid =Umax stationary plate F T j Viscosity: A shearing force of F = 10 dynes is applied to a rectangular plate of 5 x 10 cm dimensions, which sits on top of an h = 0.5 mm high column of Newtonian fluid that is initially at rest. As a result of the shearing force, the plate moves at a speed of u = 1 cm/s. (Note that 1 dyne = 1 g cm s².) a. What is the viscosity of this Newtonian fluid? b. What shearing force F would be required if the fluid column height h were doubled? c. What shearing force F would be required if the fluid column height h were halved? d. Plot the viscosity on the provided rate of shear vs. shear stress graph.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Parts a-c already posted please answer d

### Viscosity in Newtonian Fluids #### Concept Explanation Viscosity is the measure of a fluid's resistance to deformation at a given rate. It describes how thick or thin a fluid is and how easily it flows. In this demonstration, a shearing force (\( F = 10 \) dynes) is applied to a rectangular plate of dimensions \( 5 \times 10 \) cm. This setup involves a Newtonian fluid, which is a fluid where the viscosity remains constant regardless of the rate of shear. #### Diagram Description The diagram on the left illustrates a Newtonian fluid sheared between two plates. The top plate labeled "A" is a moving plate with velocity (\( u_{\text{plate}} = u_{\text{max}} \)), exerted by a force (\( \vec{F} \)). The bottom plate is stationary. The fluid has a velocity gradient (shown by arrows), starting from zero at the stationary plate (\( u_{\text{fluid}} = 0 \)) to the maximum plate velocity at the moving plate (\( u_{\text{fluid}} = u_{\text{max}} \)). The distance between the plates is \( h \). On the right side, there is a graph setup with axes labeled \( \tau \) (shear stress) and \( \dot{\gamma} \) (rate of shear), indicating a relationship yet to be plotted. #### Problem Statement **1.2** **Viscosity Problem Set:** A shearing force is applied to initiate movement in the Newtonian fluid. 1. What is the viscosity of this Newtonian fluid? 2. What shearing force \( F \) would be required if the fluid column height \( h \) were doubled? 3. What shearing force \( F \) would be required if the fluid column height \( h \) were halved? 4. Plot the viscosity on the provided rate of shear vs. shear stress graph. #### Additional Information - **Dimensions:** - Plate: \( 5 \times 10 \) cm - Fluid Column Height: \( h = 0.5 \) mm - **Velocity:** \( u = 1 \) cm/s - **Force:** \( F = 10 \) dynes - **Conversion Note:** \( 1 \text{ dyne} = 1 \text{ g cm s}^{-2} \
Transcribed Image Text:### Viscosity in Newtonian Fluids #### Concept Explanation Viscosity is the measure of a fluid's resistance to deformation at a given rate. It describes how thick or thin a fluid is and how easily it flows. In this demonstration, a shearing force (\( F = 10 \) dynes) is applied to a rectangular plate of dimensions \( 5 \times 10 \) cm. This setup involves a Newtonian fluid, which is a fluid where the viscosity remains constant regardless of the rate of shear. #### Diagram Description The diagram on the left illustrates a Newtonian fluid sheared between two plates. The top plate labeled "A" is a moving plate with velocity (\( u_{\text{plate}} = u_{\text{max}} \)), exerted by a force (\( \vec{F} \)). The bottom plate is stationary. The fluid has a velocity gradient (shown by arrows), starting from zero at the stationary plate (\( u_{\text{fluid}} = 0 \)) to the maximum plate velocity at the moving plate (\( u_{\text{fluid}} = u_{\text{max}} \)). The distance between the plates is \( h \). On the right side, there is a graph setup with axes labeled \( \tau \) (shear stress) and \( \dot{\gamma} \) (rate of shear), indicating a relationship yet to be plotted. #### Problem Statement **1.2** **Viscosity Problem Set:** A shearing force is applied to initiate movement in the Newtonian fluid. 1. What is the viscosity of this Newtonian fluid? 2. What shearing force \( F \) would be required if the fluid column height \( h \) were doubled? 3. What shearing force \( F \) would be required if the fluid column height \( h \) were halved? 4. Plot the viscosity on the provided rate of shear vs. shear stress graph. #### Additional Information - **Dimensions:** - Plate: \( 5 \times 10 \) cm - Fluid Column Height: \( h = 0.5 \) mm - **Velocity:** \( u = 1 \) cm/s - **Force:** \( F = 10 \) dynes - **Conversion Note:** \( 1 \text{ dyne} = 1 \text{ g cm s}^{-2} \
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