Fluid Mechanics

To determine whether the flow is steady or turbulent, we need to calculate the Reynolds number ( ). The Reynolds number is a dimensionless quantity used to predict flow patterns in fluid dynamics. It is given by: where:
is the density of the fluid (for water, ),
is the velocity of the fluid,
is the diameter of the pipe or tap,
is the coefficient of viscosity of the fluid.

Step 1: Calculate the velocity
The volumetric flow rate is given by: where is the cross-sectional area of the tap. The area is: Given:
Diameter ,
Volumetric flow rate . Substitute into the area formula: Now, solve for :

Step 2: Calculate the Reynolds number Substitute the values into the Reynolds number formula: Given:
,
,
,
. Substitute these values: Simplify:

Step 3: Interpret the Reynolds number
If , the flow is steady (laminar).
If , the flow is transitional.
If , the flow is turbulent.
Here, , which is greater than 6000. Therefore, the flow is turbulent. Final Answer:
The flow is:
Turbulent with Reynolds number greater than 6000