CE340 Homework#9 Due Friday, April 6th
Review Chapter 8. Complete the following:
1. Some common variables in fluid mechanics include: volume flow rate, Q, gravitational
acceleration, g, viscosity,
μ
, density,
ρ
, and a length, l. Determine the dimensions of the
following variable combinations in terms of the length, mass, and time system of basic
dimensions. Identify those groups that are dimensionless.
(a) , (b)
)/( 22 glQ )/( lQ
μ
ρ
, (c) , (d)
25 /Qgl
μ
ρ
/Ql .
2. A periodic Karman vortex street is formed when a uniform stream flows over a
circular cylinder. Use the step-by-step method to find the dimensionless relationship for
the Karman vortex shedding frequency fk as a function of free-stream velocity V, fluid
density
ρ
, fluid viscosity
μ
, and cylinder diameter D. (Ans: fk = f(Re))
Fig. 9-2
3. Consider a flow between two parallel plates (the Couette flow) separated by a distance
of h. The top plate is moving and the bottom plate remains stationary. Use the step-by-
step method to a dimensionless relationship for the horizontal velocity u, as a function
of fluid viscosity
μ
, top plate speed V, fluid density
ρ
, distance y and plate separation h.
(Ans: u/V = f(Re, y/h))
Fig. 9-3
4. The power P to drive an axial pump depends on the following variables: density of the
fluid,
ρ
, rotational speed of the rotor, N, diameter of the rotor, D, usable head, HD, and
volumetric flow rate, Q. A dimensionless relation in the form of:
),( 335 ND
Q
D
H
ND
PD
φ
ρ
=,
is to be used to guide scale model tests. A model scaled to one-third the size of the
prototype has the following characteristics: Nm = 900 rpm, Dm = 5 in, (HD)m = 10 ft, Qm
1
