**Explanation:**

The concept of a stream function is based on the principle of continuity, which states that the mass flow rate into a control volume must be equal to the mass flow rate out of the control volume. This principle is applicable to both two-dimensional and three-dimensional flow.

**Two-dimensional flow:**
In two-dimensional flow, the stream function is defined as a mathematical function that can be used to describe the flow field. It is a scalar function that is used to determine the velocity components in terms of the derivatives of the stream function. The stream function is constant along a streamline, and the streamlines represent the paths followed by fluid particles in the flow.

By using the stream function, the continuity equation can be satisfied by ensuring that the partial derivatives of the velocity components with respect to the coordinates satisfy a certain relationship. This allows for the determination of the velocity components and the flow field in two-dimensional flow.

**Three-dimensional flow:**
In three-dimensional flow, the concept of a stream function can still be applied, but it becomes more complex. In this case, the stream function is a scalar function that is defined in terms of three coordinates. The streamlines in three-dimensional flow are surfaces that are everywhere tangent to the velocity vector at each point.

However, the use of the stream function in three-dimensional flow is not as common as in two-dimensional flow. This is because three-dimensional flows are often more complex and difficult to analyze, and other mathematical techniques, such as the use of vorticity, are often employed instead.

**Uniform flow cases only:**
The concept of a stream function is not limited to uniform flow cases only. It can be applied to any type of flow, including non-uniform flows, such as flows with variable velocity or flows with obstructions. The stream function provides a useful mathematical tool for describing and analyzing fluid flow in a variety of cases.

**Irrotational flow only:**
The stream function is not limited to irrotational flow only. It can be used to describe both rotational and irrotational flow. In the case of irrotational flow, the vorticity is zero, and the stream function can be used to fully describe the flow field. In the case of rotational flow, the vorticity is non-zero, and the stream function is used in conjunction with other mathematical tools, such as the vorticity equation, to describe the flow field.