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For a pipe flow with Re=1000, the length of entrance region is L₁. For the flow with Re=1500 in the same pipe, the length of entrance region is L₂. In this case, which one of the following is true? a. L₁ = L₂

b. L₁ < L₂

c. L₁ > L₂ d. L₁ ≤ L₂

e. L₁ ≥ L₂

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Answer :

For a pipe flow with Re=1000, the length of entrance region is L₁. For the flow with Re=1500 in the same pipe, the length of entrance region is L₂. In this case, L₁ < L₂ is true.

The entrance length of a duct is the section at the start of the duct where the speed, temperature, density, and other variables are altered by the transition from motionlessness to the fluid flow caused by the sudden appearance of the duct. To put it another way, the point at which fully developed channel flow is reached is referred to as the entrance length. Because fully developed channel flow is required for many types of measurement (e.g. velocity and thermal), the entrance length must be taken into account in the testing equipment layout. This situation depicts the fact that the greater the Reynolds number (Re), the longer the entry region of a channel. As a result, alternative c is rejected since the flow region is greater in the case of Re=1500 than it is for Re =1000. However, alternative a is incorrect since we can see that the entry region length changes with Re, therefore the entry region lengths are not equal. Therefore, alternative b, L₁ < L₂, is the correct choice.

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