(a) Interpretation: Fit a line to given data using the method of least squares. Concept introduction: The method of least square for a y = ax + b line is given as, here, a and b can be calculated as, S x y = 1 n ∑ i = 1 n X i Y i S x x = 1 n ∑ i = 1 n X i 2 S x = 1 n ∑ i = 1 n X i h e n c e , a = S x y − S x S y S x x − ( S x ) 2 b = S x x S y − S x S x y S x x − ( S x ) 2

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Answer 1

Question

Chapter 2, Problem 2.48P

Interpretation Introduction

(a)

Interpretation:

Fit a line to given data using the method of least squares.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Interpretation Introduction

(b)

Interpretation:

Fit a line through the origin using the same data set.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

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Ex. HW. A vertical glass tube, 2cm ID & 5m long in heated uniformly over its length. The water enter at (200-204 C) & 68.9 bar calculated the pressure drop if the flowrate 0.15 Kg/s & the power applied as a heat to the fluid is 100KW using the homogeneous model. Given that enthalpy at inlet temp.=0.87MJ/Kg, enthalpy saturation temp (285C)=1.26 MJ/Kg and μl=0.972*10-4 Ns/m2, μG=2.89*10-5 Ns/m2, UG=2.515*10-2m3/Kg and the change in UG over range of pressure=-4.45*10-4m3/Kg/bar.

4. An experimental test rig is used to examine two-phase flow regimes in horizontal pipelines. A particular experiment involved uses air and water at a temperature of 25°C, which flow through a horizontal glass tube with an internal diameter of 25.4 mm and a length of 40 m. Water is admitted at a controlled rate of 0.026 kgs at one end and air at a rate of 5 x 104 kgs in the same direction. The density of water is 1000 kgm³, and the density of air is 1.2 kgm. Determine the mass flow rate, the mean density, gas void fraction, and the superficial velocities of the air and water. Answer: 0.02605 kgs 1, 61.1 kgm³, 0.94, 0.822 ms-1, 0.051 ms-1

Answer 2

Question

Chapter 2, Problem 2.48P

Interpretation Introduction

(a)

Interpretation:

Fit a line to given data using the method of least squares.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Interpretation Introduction

(b)

Interpretation:

Fit a line through the origin using the same data set.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 2, Problem 2.48P

Interpretation Introduction

(a)

Interpretation:

Fit a line to given data using the method of least squares.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Interpretation Introduction

(b)

Interpretation:

Fit a line through the origin using the same data set.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 2, Problem 2.48P

Interpretation Introduction

(a)

Interpretation:

Fit a line to given data using the method of least squares.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Interpretation Introduction

(b)

Interpretation:

Fit a line through the origin using the same data set.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 2, Problem 2.48P

Interpretation Introduction

(a)

Interpretation:

Fit a line to given data using the method of least squares.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Interpretation Introduction

(b)

Interpretation:

Fit a line through the origin using the same data set.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Answer 6

Chapter 2, Problem 2.48P

Interpretation Introduction

(a)

Interpretation:

Fit a line to given data using the method of least squares.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Answer 7

Chapter 2, Problem 2.48P

Interpretation Introduction

(a)

Interpretation:

Fit a line to given data using the method of least squares.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Answer 8

Interpretation Introduction

(b)

Interpretation:

Fit a line through the origin using the same data set.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Answer 9

Interpretation Introduction

(b)

Interpretation:

Fit a line through the origin using the same data set.

Concept introduction:

The method of least square for a y = ax + b line is given as, here, a and b can be calculated as,

Sxy = 1n ∑i=1nXiYiSxx =1n∑i=1nXi2Sx = 1n∑i=1nXi

hence,a = Sxy−Sx Sy Sxx − (Sx )2b = SxxSy−Sx Sxy Sxx − (Sx )2

Answer 10

Expert Solution & Answer

Answer 11

Expert Solution & Answer

Answer 12

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Answer 13

Ch. 2 - Prob. 2.1P Ch. 2 - Prob. 2.2P Ch. 2 - Prob. 2.3P Ch. 2 - Prob. 2.4P Ch. 2 - Prob. 2.5P Ch. 2 - Prob. 2.6P Ch. 2 - Prob. 2.7P Ch. 2 - Prob. 2.8P Ch. 2 - Prob. 2.9P Ch. 2 - Prob. 2.10P

Solution Summary: The author explains how the method of least squares is used to fit a line to given data.

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Chapter 2 Solutions