Air ows through a rectangular duct of dimension 1 ft 5 ft. The velocity prole
is linear, with a maximum velocity of 15 ft/s. Find the kinetic energy correction
The kinetic energy correction factor is
Flow in Conduits
Water at 20o C ( = 10 3 Ns/m2 , = 1000 kg/m3 ) ows through a 0.5-mm tube
connected to the bottom of a reservoir. The length of the tube is 1.0 m, and the
depth of water in the reservoir is 20 cm. Find the ow rate i
Calculate the density and specic weight of nitrogen at an absolute pressure of
1 MPa and a temperature of 40r C.
Ideal gas law
From Table A.2, U = 297 J/kg/K. The temperature in absolute units is W =
Consider a glass container, half-full of water and half-full of air, at rest on a laboratory table. List some similarities and dierences between the liquid (water) and
the gas (air).
1. The gas and
An aluminum cube of density 2700 kg/m3 slides with a constant speed of 20 cm/s
down a plate that is at an angle of 30r with respect to the horizontal. The plate is
covered with a stationary layer of 0.1-mm-thick oi
Dimensional Analysis and
The discharge, T> of an ideal uid (no viscous eects) through an orice depends
on the orice diameter, g, the pressure drop across the orice, s, and the uid
density. Find a nondimensional relationshi
Varied Flow in Open
Water ows in a circular concrete pipe (Mannings q = 0=012) with a depth that is
half of the pipe diameter (0.8 m). If the slope is 0.004, nd the ow rate.
The ow rate is obtained from the Chezy
Water at 20o C is discharged from a nozzle onto a plate as shown. The ow rate of
the water is 0.001 m3 @s, and the diameter of the nozzle outlet is 0.5 cm. Find the
force necessary to hold the plate in place.
A propeller is to be selected for a light airplane with a mass of 1500 kg which
will cruise at 100 m/s at an altitude where the density is 1 kg/m3 The lift-to-drag
ratio at cruise conditions is 30:1, and the engine r
Control Volume Approach
and Continuity Principle
A 10-cm-diameter pipe contains sea water that ows with a mean velocity of 5
m/s. Find the volume ow rate (discharge) and the mass ow rate.
The discharge is
where Y is the
Flowing Fluids and Pressure
A ow moves in the cfw_-direction with a velocity of 10 m/s from 0 to 0.1 second
and then reverses direction with the same speed from 0.1 to 0.2 second. Sketch
the pathline starting from cfw_ = 0
Velocity in an air ow is to be measured with a stagnation tube that has a resolution of 0.1-in. H2 O. Find the minimum uid speed in ft/s that can be measured.
Neglect viscous eects and assume that the air is at ro
Methane at 25o C (U = 518 J/kg/K, n = 1=31) is owing in a pipe at 400 m/s.
Is the ow subsonic, sonic, supersonic, or hypersonic?
The speed of sound in methane is
f = nUW = 1=31 518 298
= 450 m/s
For a lake, nd the depth k at which the gage pressure is 1 atmosphere.
specic weight of water is 62.3 lbf/ft3 .
At the free surface of the lake, pressure will be ssurface = 1=0 atm absolute or 0.0
Drag and Lift
Air with a speed of Yr ows over a long bar that has a 15r wedge-shaped crosssection. The pressure variation, as represented using the coe!cient of pressure, is
shown in the following sketch. On the west face of the ba