University of technology____________ Fluid Flow __________________ Dr. Asawer A. Alwasity
Tutorial Sheet
No. 2
Q1) At low velocities (laminar flow), the volume flow Q through a small-bore tube is
a function only of the tube radius R, the fluid viscosity , and the pressure drop per unit
tube length dp/dx. Using the pi theorem, find an appropriate dimensionless
relationship.
Q2) The capillary rise h of a liquid in a tube varies with tube diameter d, gravity g,
fluid density , surface tension , and the contact angle . (a) Find a dimensionless
statement of this relation. (b) If h=3 cm in a given experiment, what will hbe in a
similar case if the diameter and surface tension are half as much, the density is twice
as much, and the contact angle is the same?
Q3)Under laminar conditions, the volume flow Q through a small triangular-section
pore of side length b and length Lis a function of viscosity , pressure drop per unit
length,and b. Using the pi theorem, rewrite this relation in dimensionless form. How
does the volume flow change if the pore size b is doubled?
Q4) The power input P to a centrifugal pump is assumed to be a function of the
volume flow Q, impeller diameter D, rotational rate, and the density and viscosity of
the fluid. Rewrite this as a dimensionless relationship. Hint: Take rotation speed and
density, and D as repeating variables.
Q5)The heat-transfer rate per unit area q to a body from a fluid in natural or
gravitational convection is a function of the temperature difference T, gravity g, body
length L, and three fluid properties: kinematic viscosity , conductivity k, and thermal
expansion coefficient J . Rewrite in dimensionless form if it is known that g and J
appear only as the product gJ.
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University of technology____________ Fluid Flow __________________ Dr. Asawer A. Alwasity
Q6)When a viscous fluid is confined between two long concentric cylinders as in
Fig., the torque per unit length Trequired to turn the inner cylinder at angular
velocity is a function of angular velocity, cylinder radii a and b, and
viscosity . Find the equivalent dimensionless function. What happens to the
torque if both a and b are doubled?
Q7) problem (4-1) in fluid flow book
Q8) problem (4-24) in fluid flow book
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