Question

prandtl mixing length for turbulent flow through pipe is​

Answer 1

$\huge\purple{\mathbb{AnsWer:}}$

It is interesting to note in advance that von KArmAn's similarity hypothesis is obtained as a special case of the present model. REFORMULATION OF PRANDTL'S. MIXING LENGTH THEORY.

♥ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘs ʏᴏᴜ. ㋛

♥ᴘʟᴇᴀsᴇ ғᴏʟʟᴏᴡ ᴍᴇ ᴀɴᴅ ᴍᴀʀᴋ ᴀs ʙʀᴀɪɴʟɪᴇsᴛ.

Answer 2

Answer:

The shear stress can be treated as linear in both axes i.e, zero at center and varying linearly up to the wall.

Explanation:

According to Prandtl, the mixing length l is the distance in the transverse direction between two layers that allows lumps of fluid particles from one layer to reach the other layer and the particles to be mixed in the other layer with the same momentum in the direction of x.

$u' = l\frac{du}{dy}$  and $v' = l\frac{du}{dy}$

The above equation gives velocity fluctuation in x and y direction in terms of mixing length l.

$u'$ x $y' = l\frac{du}{dy}$  x $l\frac{du}{dy}$   = $l^{2} (\frac{du}{dy} )^{2}$

Turbulence shear stress is given by :

τ$_{t}$ = ρ$u'v'$ = ρ$l^{2} (\frac{du}{dy} )^{2}$

Total shear stress acting on the field is:

τ = τ${v}$ + τ${t}$

τ = μ$\frac{du}{dy}$ + ρ$l^{2} (\frac{du}{dy} )^{2}$

Therefore, mixing length l is the distance measured in the transverse direction (perpendicular to flow), where lumps reach the other layer and particles are mixed in the longitudinal direction (parallels to flow).

#SPJ3