The specific speed of a fluid machine refers to a type-number that is representative of its performance. It is often used to compare and classify different types of fluid machines such as pumps, turbines, and compressors. The specific speed is a dimensionless parameter that can provide valuable information about the machine's operating characteristics and efficiency.

The specific speed is calculated using the following formula:

Ns = (N√Q) / (H^3/4)

Where:
- Ns is the specific speed
- N is the rotational speed of the machine
- Q is the volumetric flow rate of the fluid
- H is the head under which the machine operates

Now let's discuss why option 'B' is the correct answer:

1. The speed of a machine of unit dimensions:
This option is incorrect because the specific speed is not related to the physical speed of the machine. It is a type-number that represents the machine's performance, not its actual speed.

2. A type-number representative of its performance:
This option is correct. The specific speed is a dimensionless parameter that provides information about the performance characteristics of a fluid machine. It takes into account the rotational speed, flow rate, and head of the machine to provide a numerical value that can be used for comparison and classification purposes.

3. Specific to the particular machine:
This option is incorrect. The specific speed is not specific to a particular machine. It is a parameter that can be calculated for any fluid machine as long as the necessary input values (rotational speed, flow rate, and head) are known.

4. Depends only upon the head under which the machine operates:
This option is incorrect. While the head is one of the parameters used in the calculation of specific speed, it is not the only factor. The specific speed also takes into account the rotational speed and flow rate of the fluid. Therefore, it depends on all three of these factors, not just the head.

In conclusion, the specific speed of a fluid machine is a type-number that represents its performance characteristics. It is calculated using a formula that takes into account the rotational speed, flow rate, and head of the machine. Option 'B' is the correct answer as it accurately describes the specific speed of a fluid machine.