The normal distribution version The head loss due to sudden enlargement in a pipeline, as shown in Figure P6.1, can be cal-culated ash, =2gA2where A, and V, are the area and velocity of the fluid in the smaller pipe, and A, and V, arethe area and velocity of the fluid in the larger pipe. If A/A2 is a constant of magnitude 0.5and Vi has an normal distribution with mean of Hv,, determine the distribution of h-V1A1V2A2Figure P6.1 Sudden Expansion of Flowin a Pipe

where A, and V, are the area and velocity of the fluid in the smaller pipe, and. the area and velocity of the fluid in the larger pipe. If A1/A2 is a constant of n and Vi has an normal distribution with mean of Hv,, determine the distri V1 V2 A1 A2 Figure P6.1 Sudden Expar in a Pipe

where A, and V, are the area and velocity of the fluid in the smaller pipe, and. the area and velocity of the fluid in the larger pipe. If A1/A2 is a constant of n and Vi has an normal distribution with mean of Hv,, determine the distri V1 V2 A1 A2 Figure P6.1 Sudden Expar in a Pipe

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

The normal distribution version

The head loss due to sudden enlargement in a pipeline, as shown in Figure P6.1, can be cal-
culated as
h, =
2g
A2
where A, and V, are the area and velocity of the fluid in the smaller pipe, and A, and V, are
the area and velocity of the fluid in the larger pipe. If A/A2 is a constant of magnitude 0.5
and Vi has an normal distribution with mean of Hv,, determine the distribution of h-
V1
A1
V2
A2
Figure P6.1 Sudden Expansion of Flow
in a Pipe

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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