Question

A turbine agitator having six flat blades and a disk has a diameter of 0.203 m and its used in a tank having a diameter of 0.61 m and height of 0.61 m. the width W = 0.0405 m Four baffles are used having a width of 0.051 m. The turbine operates at 275 rpm in a liquid having a density of 909 kg/m³ and viscosity of 0.020 Pa.s. a) Calculate the kW power of the turbine and kW/m³ of volume. b) Scale up this system to a vessel having a volume of 100 times the original for the case of equal mass transfer rate. (35 marks)

Answer 1

The problem involves calculating the power of a turbine agitator and scaling it up while maintaining the same mass transfer rate. The power can be calculated using fluid dynamics principles and empirical correlations. The scaling process involves comparing the Reynolds number for the two systems.

Step-by-step explanation:

This problem involves engineering principles related to turbine agitators and fluid dynamics. Firstly, to calculate the power and the power per unit volume of the turbine agitator, we are given relevant parameters such as the density and viscosity of the liquid, speed of the turbine in rotations per minute (rpm), and dimensions of the turbine and tank.

However, the equation for the power depends not only on the parameters given but also on the specific design of the turbine.

A commonly used equation for the power of a rotating object in a fluid is P = ρ * n³ * D⁵, where ρ is the fluid density, D is the diameter of the turbine, and n is the speed of rotation.

Secondly, when we talk about scaling up the system maintaining the same mass transfer rate, it means that we need to consider the effect of scale on the operation of the turbine.

This typically involves comparing the Reynolds number, a dimensionless number which describes the type of flow in the system, for the two systems. Again, the equations to do this will depend on the specific design of the system and can be quite complex in practice.

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