Chapter 8, Problem 1CP

How is the hydrodynamic entry length defined for flow in a pipe? Is the entry length longer in laminar or turbulent flow?

To determine

The hydrodynamic entry length for the laminar flow in the pipe.

The hydrodynamic entry length for the turbulent flow in the pipe.

The entry length is longer in laminar or turbulent flow.

Answer to Problem 1CP

The hydrodynamic entry length for the laminar flow in the pipe is $0.05D\mathrm{Re}$.

The hydrodynamic entry length for the turbulent flow in the pipe is $1.359D{\left(\mathrm{Re}\right)}^{\frac{1}{4}}$.

The entry length is longer in the laminar flow as compare to the turbulent flow.

Explanation of Solution

The growth of boundary layer thickness remains along the flow direction until the boundary layer reaches the pipe center. The hydrodynamic entrance region is defined as the region from the inlet of pipe to the point at which the boundary layers merges at the centerline of the pipe and the hydrodynamic entry length is the length of the hydrodynamic entrance region.

Write the expression for the hydrodynamic entry length for the laminar flow in the circular pipe.

  $L_{h,\text{laminar}}=0.05D\mathrm{Re}$...... (I)

Here, hydrodynamic entry length for the laminar flow in the circular pipe is $L_{h,\text{laminar}}$, diameter of the pipe is $D$ and Reynolds number for the flow is $\mathrm{Re}$.

Write the expression for the hydrodynamic entry length for the turbulent flow in the circular pipe.

  $L_{h,\text{turbulent}}=1.359D{\left(\mathrm{Re}\right)}^{\frac{1}{4}}$...... (II)

Here, hydrodynamic entry length for the turbulent flow in the circular pipe is $L_{h,\text{turbulent}}$, diameter of the pipe is $D$ and Reynolds number for the flow is $\mathrm{Re}$.

The hydrodynamic entry length for the laminar flow is longer than the hydrodynamic entry length for the turbulent flow at the high Reynolds numbers.

Conclusion:

The hydrodynamic entry length for the laminar flow in the pipe is $0.05D\mathrm{Re}$.

The hydrodynamic entry length for the turbulent flow in the pipe is $1.359D{\left(\mathrm{Re}\right)}^{\frac{1}{4}}$.

The entry length is longer in the laminar flow as compare to the turbulent flow.