(a) For a pipe flow, define the length of the entrance region flow.

(b) For a pipe flow with [tex]\text{Re}=1000[/tex], the length of the entrance region is [tex]L_1[/tex]. For the flow with [tex]\text{Re}=1500[/tex] in the same pipe, the length of the entrance region is [tex]L_2[/tex]. In this case, which one of the following is true?

A. [tex]L_1 = L_2[/tex]
B. [tex]L_1 < L_2[/tex]
C. [tex]L_1 > L_2[/tex]
D. [tex]L_1 \leq L_2[/tex]
E. [tex]L_1 \geq L_2[/tex]

(a) The entrance region flow is defined as the length of the pipe section that is immediately upstream of the entrance. where the flow undergoes significant changes and adapts to the conduit.

This region is characterized by the development of velocity and temperature profiles, which change as the fluid adapts to the conduit and any changes in cross-section or fluid properties that may occur.

(b) For a pipe flow with Re=1000, the length of entrance region is L1, and for the flow with Re=1500 in the same pipe, the length of entrance region is L2.

In this case, the correct option is c. L1 > L2.

This is due to the fact that the Reynolds number (Re = 1500) is higher in the second flow, implying that there is a stronger effect of inertia forces on the flow, which resulting in a shorter entrance region compared to the flow with Re = 1000.

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