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
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
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
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
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
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
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
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.
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
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
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