## Viscosity Shear-Stress

### GATE-CH-1993-9-c-fm-2mark

1993-9-c-fm

Match the following: The shear stress vs. velocity gradient characteristics are shown in figure.

• I.

• II.

• III.

• IV.

### GATE-CH-1988-2-ii-fm-1mark

1988-2-ii-fm

For pseudoplastic fluids, increase in shear rate

• increases the apparent viscosity

• decreases the apparent viscosity

• has no effect on apparent viscosity

• has unspecified effect

### GATE-CH-1989-2-i-c-fm-1mark

1989-2-i-c-fm

For a dilatant fluid, the magnitude of the slope of the shear stress versus the velocity gradient curve ––––- with increasing velocity gradient.

• increases

• decreases

• remains unchanged

• may decrease or increase

### GATE-CH-1994-1-j-fm-1mark

1994-1-j-fm

The shear stress–shear rate relationship for a liquid whose apparent viscosity decreases with increasing shear rate is given by

• $$\displaystyle \tau _{yx} = -m\left [\frac {dv_x}{dy}\right ]^{n-1}\frac {dv_x}{dy}$$ for $$n <1$$

• $$\displaystyle \tau _{yx} = -m\left [\frac {dv_x}{dy}\right ]^{n}$$ for $$n =1$$

• $$\displaystyle \tau _{yx} = -m\left [\frac {dv_x}{dy}\right ]^{n-1}\frac {dv_x}{dy}$$ for $$n >1$$

• $$\displaystyle \tau _{yx} = -m\frac {dv_x}{dy} + \tau _o$$

### GATE-CH-2001-2-6-fm-2mark

2001-2-6-fm

A Bingham fluid of viscosity $$\mu$$ = 10 Pa.s, and yield stress $$\tau _o$$ = 10 kPa, is sheared between flat parallel plates separated by a distance 10$$^{-3}$$ m. The top plate is moving with a velocity of 1 m/s. The shear stress on the plate is

• 10 kPa

• 20 kPa

• 30 kPa

• 40 kPa

[Index]

### GATE-CH-2003-10-fm-1mark

2003-10-fm

A lubricant 100 times more viscous than water would have a viscosity (in Pa.s)

• 0.01

• 0.1

• 1

• 10

### GATE-CH-2004-49-fm-2mark

2004-49-fm

Viscosity of water at 40oC lies in the range of

• $$1\times 10^{-3}$$ - $$2\times 10^{-3}$$ kg/(m.s)

• $$0.5 \times 10^{-3}$$ - $$1 \times 10^{-3}$$ kg/(m.s)

• 1 - 2 kg/(m.s)

• 0.5 - 1 kg/(m.s)

### GATE-CH-2005-12-fm-1mark

2005-12-fm

Match the following types of fluid (in group I) with their respective constitutive relations (in group II), where $$\tau$$ is the stress and $$\dot {\gamma }$$ is the strain rate.

Group I Group II
(P) Pseudoplastic (I) $$\tau = \mu \dot {\gamma }$$
(Q) Bingham plastic (II) $$\tau = \tau _o + K\dot {\gamma }$$
(III) $$\tau = K|\dot {\gamma }|^n; \quad n < 1$$
(IV) $$\tau = K|\dot {\gamma }|^n; \quad n > 1$$

• P-I, Q-IV

• P-IV, Q-I

• P-II, Q-III

• P-III, Q-II

### GATE-CH-2006-38-fm-2mark

2006-38-fm

A fluid obeying the constitutive equation $\tau = \tau _o + K \left (\frac {dv_x}{dy}\right )^{\frac {1}{2}}, \quad \tau > \tau _o$ is held between two parallel plates a distance $$d$$ apart. If the stress applied to the top plate is $$3\tau _o$$, then the velocity with which the top plate moves relative to the bottom plate would be

• $$\displaystyle 2 \left (\frac {\tau _o}{K}\right )^2d$$

• $$\displaystyle 3 \left (\frac {\tau _o}{K}\right )^2d$$

• $$\displaystyle 4 \left (\frac {\tau _o}{K}\right )^2d$$

• $$\displaystyle 9 \left (\frac {\tau _o}{K}\right )^2d$$

### GATE-CH-2013-10-fm-1mark

2013-10-fm

The apparent viscosity of a fluid is given by $$0.007 \left (\dfrac {dV}{dy}\right )^{0.3}$$ where $$\left (\dfrac {dV}{dy}\right )$$ is the velocity gradient. The fluid is

• Bingham plastic

• dilatant

• pseudoplastic

• thixotropic

[Index]

### GATE-CH-2014-13-fm-1mark

2014-13-fm

Which of the following statements are CORRECT?

• [P.] For a rheopectic fluid, the apparent viscosity increases with time under a constant applied shear stress
• [Q.] For a pseudoplastic fluid, the apparent viscosity decreases with time under a constant applied shear stress
• [R.] For a Bingham plastic, the apparent viscosity increases exponentially with the deformation rate
• [S.] For a dilatant fluid, the apparent viscosity increases with increasing deformation rate

• P and Q only

• Q and R only

• R and S only

• P and S only

### GATE-XE-2012-B-14-fm-2mark

XE-2012-B-14-fm

The figure given below shows typical non-dimensional velocity profiles for fully developed laminar flow between two infinitely long parallel plates separated by a distance $$a$$ along $$y$$-direction. The upper plate is moving with a constant velocity $$U$$ in the $$x$$-direction and the lower plate is stationary.

Match the non-dimensional velocity profiles in column I with the pressure gradients in column II.

Column I Column II
P. profile I 1. $$\dfrac {\partial P}{\partial x} > 0$$
Q. profile II 2. $$\dfrac {\partial P}{\partial x} < 0$$
R. profile III     3. $$\dfrac {\partial P}{\partial x} = 0$$

• P-2; Q-3; R-1

• P-3; Q-2; R-1

• P-3; Q-1; R-2

• P-1; Q-2; R-3

### GATE-CH-2012-52-53-fm-4mark

2012-52-53-fm

A Newtonian fluid of viscosity $$\mu$$ flows between two parallel plates due to the motion of the bottom plate (as shown below), which is moved with a velocity $$V$$. The top plate is stationary.

(i) The steady, laminar velocity profile in the $$x$$-direction is

{#1}

(ii) The force per unit unit area (in the $$x$$-direction) that must be exerted on the bottom plate to maintain the flow is

{#2}

[Index]

Last Modified on: 02-May-2024

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