flow momentum. An equation is derived in Ref. (Eq. 2.83) which gives the relatio

Question

flow momentum. An equation is derived in Ref. (Eq. 2.83) which gives the relationship between the drag per unit span of an immersed body based on the local velocity in the wake in an incompressible fluid as (10) where ul and u2 are the freestream and local velocity respectively and is the density of the fluid. The beginning and ending coordinates of the vertical cross section is denoted by yi and y2. The velocity measurement must be performed several diameter lengths behind the body so as to ensure the wake has returned to the tunnel freestream velocity Using Eq. (10), derive the following expression for coefficient of drag C wane uaverse versus y-location. (12) where q and qo are the local and freestream values of dynamic pressure, d is the cylinder diameter, and yi and y2 are the beginning and ending coordinates of the vertical pressure traverse respectively

Explanation / Answer

given

D = rho*integrate(u2(u1 - u2)dy) form y2 to y1

now, Cd = D/qo
qo = 0.5*rho*u1^2*d
consider
q = 0.5*rho*u2^2*d

hence
Cd = rho*integrate(u2(u1 - u2)dy/qo) form y2 to y1
Cd = rho*integrate(u2(u1 - u2)dy/0.5*rho*u1^2*d) form y2 to y1
Cd = (2/d)*integrate(u2/u1 - u2^2/u1^2)dy) form y2 to y1

now, u2/u1 = sqroot(q/qo)
hence
Cd= (2/d)*integrate(sqrt(q/qo) - q/qo)dy) form y2 to y1

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

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