Fall’23
IMU 311 Fluid Mechanics I
Assignment 4
Due Date: 02/01/2024
1. Considering 2-D, plane Navier-Stokes equation form as given
 V

+V V   p   2 V
 t


a) Obtain non-dimensional form using the following reference variables:
Reference velocity U, reference length L, reference pressure=μU/L
b) Simplify the equation you obtained in part (a) for creep flow (Creep flow means that viscous
forces become extremely dominant when compared to the inertial forces.)
c) Using the stream function u 



, show that  2 w  0 is valid for the equation you
, v
y
x
obtained in part (b).
2. A constant-thickness film of viscous liquid flows in steady, incompressible, laminar motion down
a plate inclined at angle θ, as in the figure. The velocity profile is
𝑢 = 𝐶𝑦(2ℎ − 𝑦),
𝑣=𝑤=0
a) Find the constant C in terms of the specific weight γ and viscosity μ and the angle θ.
b) Find the volume flux Q per unit width in terms of these parameters.
3. The velocity component in y-direction of an incompressible fluid for a two-dimensional, steady,
inviscid, irrotational flow field is given as
𝑣 = 3𝑥 − 6𝑥 − 3𝑦
where v is velocity in m/s. If the velocity of the flow and the pressure is 1 m/s and Patm, respectively,
when x= 0 and y=0. Assume that the gravity acts in -z direction and the density of the fluid is ρ0.
a) Find the velocity component in x-direction.
b) Find the flow velocity at x=1 m and y=1 m.
c) Find the pressure function.