Question

Hi, I need help with this Fluid Mechanics question. Please show all the steps.

Thank you

PROBLEM 1: Consider the steady flow in a water pipe joint shown in the diagram. The areas are: A1 = 0.2m2, A2 = 0.2m2, and A3 = 0.15m². In addition, fluid is lost out of a hole at (4), estimated at a rate of 0.1 m3/s. The average speeds at sections (1) and (3) are V1 = 5 m/s and V2 = 12 m/s respectively. Find the velocity at section (2). 304

Answer 1

Velocity at section (2) is 4.5 m/s and the flow is entering at that section.

Hope it helps.

We know flow enters from I and leaves at 3. Let us assume the flow also leaves from 2 (direction Outword) Taking Flow entering as negative and leaking os Positive, we con unite -0, + O2 + O2 + + : 0 (Net flow will be zero for the steddy ' flow ) we know = AV So, - Av. + AzV2 + A₂ kg + Q4 = 0 Substitute values -60:2x5) + f0:2xV2) + f0 15x12) +0.1=0 - V2 = -0.9 112 - - 4.5 m/s we had considered flow of 2 to be outward fpositive) But we are getting 12 negative Soy Flow ot 2 will be Lin ward (entening) 0.2