Homework SourseThe hydraulic head loss by friction in a pipe may be determi
The hydraulic head loss by friction in a pipe may be determined by the Darcy-Weisbach equation as follows:
where L and D are length and diameter of the pipe, g = 32.17 ft/s2 is acceleration due to gravity, and f is a friction factor that depends on the relative roughness of the pipe and the Reynold’s number of the flow. The pipe under consideration has L = 100 ft and the following uncertain properties:
where z is the elevation change (20 ft) and cv is a constant that depends on temperature and elevation (= 30.69 ft).
Answer the following questions:
a. Determine the mean and standard deviation of hL by first-order approximation (to a nonlinear function of multiple random variables).
c. Making assumptions that appear reasonable to you, compute the probability of failure (A< 0).
V2L hL= J D(2g)Solution
the dracy-weisbach eqation contains a dimensionless friction factor, known as the darcy friction factor. this is also varoiusly called the darcy-weisbach friction factor, friction factor, resistance coefficient or flow coefficient.
in a cylinderical pipe of uniform diameter D,flowing full, the pressure loss due to viscous effects deltaP is propotional to length L and can be chaacterized by the dracy-weisbach equation.
deltaP/L=fD.row/2.(v)2/D,
where the pressure loss per unit length deltaP/L is a function of
row the density of thefluid(kg/m3)
D the hydraulic diameter of the pipe
(v) the mean flow velocity experimentally measured as the volumetric flow rate Q per unit cross sectional wetted area
FD the darcy friction factor FD is called flow coefficient ladma by some
