Fluid tutorial 1_ans dr.waleed. 01004444149

1. Tutorial (1) Dr.waleed, Mob. 0100 4444 149 Page (1)
Tutorial (1)
(1) Variables such as volume flow rate (𝑄), viscosity (𝜇), density (𝜌), gravitational
acceleration (𝑔), and pipe diameter (𝐷) are common in fluid mechanics.
Which of the following combinations for these variables are dimensionless?
Solution
(i)
{( ) }
* +* +
So this variable is not a dimensionless
(ii)
{ }{ }
* +* +
=1
So this variable is a dimensionless
(iii)
{ }{ }
*( ) +
{ }
* +
=1
So this variable is a dimensionless
(2) In a Test, for dimensional homogeneity, the following formula for volume flow Q
through a hole of diameter D in the side of a tank whose liquid surface is a distance h
above the hole position:
𝑄 𝐷 √𝑔
Where (g) is the acceleration of gravity. What are the dimensions of the constant 0.68?
Solution
By writing the equation in dimension form
*𝑄+ * + * + * + {( ) }
*𝑄+ * + * + * +
So the constant (0.68) is indeed dimensionless, and the formula is dimensionally
homogenous and can be used with any system of units

2. Tutorial (1) Dr.waleed, Mob. 0100 4444 149 Page (2)
(3) The Stokes-Oseen formula [18] for drag force F on a sphere of diameter D in a
Fluid stream of low velocity V, density 𝜌 and viscosity 𝜇 is
𝜇𝐷 𝜌 𝐷
Is this formula dimensionally homogeneous?
Solution
* + * +* +* +* + * +* +* +* +
* + * + * +
Therefor the Stokes-Oseen formula is a dimensionally homogenous
(4) For low-speed (laminar) steady flow through a circular pipe, as shown in figure, the
velocity u varies with radius and takes the form
𝜇
( )
Where 𝜇 is the fluid viscosity and 𝛥 is the pressure drop from entrance to exit.
What are the dimensions of the constant 𝐵?
Solution
𝜇
( )
* + 𝐵
* +
* +
* +
* + * +

3. Tutorial (1) Dr.waleed, Mob. 0100 4444 149 Page (3)
(5) The force, F, of the wind blowing against a building is given by,
𝜌
Where ( ) is the wind speed, (𝜌) the density of the air, ( ) the cross-sectional area of the
building, and ( 𝐷) is a constant termed the drag coefficient. Determine the dimensions of
the drag coefficient.
Solution
𝜌
* + * +* +* +* +
* + * +* +
So the drag coefficient constant is indeed dimensionless, and the formula is
dimensionally homogenous and can be used with any system of units