10. The Reynolds number (Re) is an important dimensionless quantity in fluid mechanics that is used to help predict flow patterns in different fluid flow situations. It is widely used in applications ranging from liquid flow in a pipe to the passage of air over an aircraft wing. It is also related to approximating the solutions of partial differential equations in finance using the finite difference method, as we shall see in later chapters (correctiondominated problems). The number is defined by:

pvL

????

where:

 ???? is the density of the fluid (kg/m3)

 v is a characteristic velocity of the fluid with respect to the object (m/s)

 L is a characteristic linear dimension (m)

 ???? is the dynamic viscosity of the fluid (kg/(m⋅s)).

Prove that the Reynolds number is a dimensionless quantity.