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.

                                                                                           Figure Q1

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

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 m³.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.