Tank Drainage
A large open vertical tank has three small, smooth, well-rounded orifices spaced equidistantly at ¼h, ½h, ¾h up from the bottom of the tank (Fig. Q1). Water is continuously added to the tank, and an overflow tube maintains the water level constant at h. Derive a relationship between the places where the three jets hit the ground.
Q.2 Apparent Viscosity
Rheological data for a test fluid from a rheometer is presented in Table Q2. The data was obtained by first increasing the shear rate up to 200 s^{-1} and measuring the shear stress (1.) and then decreasing the shear rate and measuring the new stress stress (2.). Plot the data for shear stress with shear rates. On the same graph, determine and plot the apparent viscosities with shear rate. Describe accurately this type of fluid. Explain why the profiles are not identical.
Table Q2
Shear rate s^{-1}
1. Shear stress Nm^{-2}
2. Shear stress Nm^{-2}
5
116
74
18
255
203
32
353
304
45
440
392
59
520
474
72
598
548
86
674
617
99
747
684
113
817
750
126
880
812
139
948
874
153
1008
937
166
1063
999
180
1114
1065
193
1160
1133
200
1181
1172
Q.3 Laminar Flow
A process uses an oil of density 800 kg.m^{-3} and viscosity 80 mPa.s at a rate of 0.72 m^{3}.h^{-1}. The feed pipe splits into two smaller pipes and both discharge freely into the process. One pipe has an inner diameter of 5.0 cm and length of 20 m while the other has an inner diameter of 2.5 cm and length of 10 m.
1. Determine the rate of flow in each pipe.
2. Confirm laminar flow in each pipe by calculating the Reynolds number.