Question

Two large flat plates are separated by a thin glycerin layer that is 5 mm thick and a temperature of 20° C. A force is applied to the top plate such shear stress = 26 Pa is generated. How fast will the top plate move relative to the bottom plate after a constant velocity is attained?

Answer 1

As we know the equation for torque

$\\\tau = \mu \frac{V}{h} \\\\\text{Where,} \\\\\mu =\text{Viscosity of glycerin}=1.41 \ \frac{Ns}{m^2} \ \text{ At 20 degree and 100}\% \text{ Glycerin} \\\\V=\text{Velocity } \\\\\tau =\text{shear stress }=26 Pa \\\\h=\text{Thickness }=5mm=5*10^{-3} \ m$

So,

$\\v=\frac{\tau h}{\mu}=\frac{26*5*10^{-3}}{1.41} \\\\v=0.092198582 \ \ m/s$

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Table of the viscocity of glycerin at diff temp the unit of viscocity is

mNs 2 m 10-3Ns 2 m

	Temperature (C)
												Glycerine per cent weight	0	10	20	30	40	50	60	70	80	90	100
0	1.792	1.308	1.005	0.8007	0.656	0.5494	0.4688	0.4061	0.3565	0.3165	0.2838
10	2.44	1.74	1.31	1.03	0.826	0.68	0.575	0.5	—	—	0
20	3.44	2.41	1.76	1.35	1.07	0.879	0.731	0.635	—	—	0
30	5.14	3.49	2.5	1.87	1.46	1.16	0.956	0.816	0.69	—	—
40	8.25	5.37	3.72	2.72	2.07	1.62	1.3	1.09	0.918	0.763	0.668
50	14.6	9.01	6	4.21	3.1	2.37	1.86	1.53	1.25	1.05	0.91
60	29.9	17.4	10.8	7.19	5.08	3.76	2.85	2.29	1.84	1.52	1.28
65	45.7	25.3	15.2	9.85	6.8	4.89	3.66	2.91	2.28	1.86	1.55
67	55.5	29.9	17.7	11.3	7.73	5.5	4.09	3.23	2.5	2.03	1.68
70	76	38.8	22.5	14.1	9.4	6.61	4.86	3.78	2.9	2.34	1.93
75	132	65.2	35.5	21.2	13.6	9.25	6.61	5.01	3.8	3	2.43
80	255	116	60.1	33.9	20.8	13.6	9.42	6.94	5.13	4.03	3.18
85	540	223	109	58	33.5	21.2	14.2	10	7.28	5.52	4.24
90	1310	498	219	109	60	35.5	22.5	15.5	11	7.93	6
91	1590	592	259	127	68.1	39.8	25.1	17.1	11.9	8.62	6.4
92	1950	729	310	147	78.3	44.8	28	19	13.1	9.46	6.82
93	2400	860	367	172	89	51.5	31.6	21.2	14.4	10.3	7.54
94	2930	1040	437	202	105	58.4	35.4	23.6	15.8	11.2	8.19
95	3690	1270	523	237	121	67	39.9	26.4	17.5	12.4	9.08
96	4600	1580	624	281	142	77.8	45.4	29.7	19.6	13.6	10.1
97	5770	1950	765	340	166	88.9	51.9	33.6	21.9	15.1	10.9
98	7370	2460	939	409	196	104	59.8	38.5	24.8	17	12.2
99	9420	3090	1150	500	235	122	69.1	43.6	27.8	19	13.3
100	12070	3900	1410	612	284	142	81.3	50.6	31.9	21.3	14.8