A boundary layer is a region of reduced velocity in a viscous fluid t is adjacen

Question

A boundary layer is a region of reduced velocity in a viscous fluid t is adjacent to a wetted surface. Assume t , in the figure below, the incoming velocity is uniformly distributed with a value of U0. At some distance downstream, x, the velocity can be approximated with a power law: U = U0(y / infinity)1/7. By applying the integral x-momentum equation to locations (1) and (2), calculate the momentum flux deficit between the two locations. (Do this by defining normal faces oriented in the positive x-direction at (1) and (2) with a height of infinity and width of w, and then comparing the two fluxes.)

Explanation / Answer

Momentum of incoming fluid at location 1 = [(w)U0]U0 = wU02

Momentum of outgoing fluid at location 2 = [Integral ((w dy)U)U ]0

= w [Integral (U2 dy)]0

= w [Integral (U02 (y/)2/7 dy)]0

= 7/9*wU02/2/7 [y9/7]0

= 7/9*wU02/2/7 [9/7]

= 7/9*wU02

Momentum flux deficit = wU02 - 7/9*wU02

= 2/9*wU02

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.