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Air whose density is $0.078 \mathrm{lbm} / \mathrm{ft}^{3}$ enters the duct of an air-conditioning system at a volume flow rate of $450 \mathrm{ft}^{3} / \mathrm{min}$ If the diameter of the duct is 10 in, determine the velocity of the air at the duct inlet and the mass flow rate of air.

Air whose density is $0.078 \mathrm{lbm} / \mathrm{ft}^{3}$ enters the duct of an air-conditioning system at a volume flow rate of $450 \mathrm{ft}^{3} / \mathrm{min}$ If the diameter of the duct is 10 in, determine the velocity of the air at the duct inlet and the mass flow rate of air.

Thermodynamics: An Engineering Approach

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Penny Riley verified

Numerade educator

Question 8 The phase velocity of ripples on a liquid surface is ( sqrt{frac{2 pi S}{lambda ho}} ), where ( S ) is the surface tension and ( ho ) is the density of the liquid. (a) Find the phase velocity as a function of ( k ). Hence, find the expression for ( omega ). (b) Find the group velocity as a function of ( k ). (c) Find the relation between group and phase velocities.

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ANSWERED

Sahil Kumar verified

Numerade educator

Question 4 In many devices involved in energy industries, a fluid (liquidor gas) flows through a pipe. If the cross-sectional area ofa pipe is 2.0 m², and the fluid in it has a speed of 1.5 m/s, (a) What is the volume flow rate in m³/s? (i.e.,what volume of fluid pass through any cross-section of the pipe every second?) (b) What mass of fluid passes through any cross-section of thepipe every second, if the fluid has a density of 1.0×10³ kg/m³? Question 5 Use the Bernoulli equation to calculate the pressure drop required to force a water flow that is originally moving at 20 ft/s in a 2 inch diameter pipe through a constriction into a 1 inch diameter pipe while simultaneously dropping 3 ft in elevation. Question 6 Find Buoyant force Using Archimedes principle replaced value 500 cm³ the density of liquid = 1.3 g/cm³, what is the mass? Question 7 Given that a source and sink are in a uniform field of U = 5 m/s, and the source and sink are located at (0, -2) and (0, 2) respectively. The source has a strength of 5 m²/s and the sink has a strength of -40m²/s. (a) Find the magnitude of the velocity at a point on the x-axis at (-4,0) (b) Find the direction of the velocity at the point (-4,0) (c) If the uniform flow is removed, and the sink is now replaced with a source of 40 m²/s, determine the location of the stagnation point in the flow field

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Rahul Kumar verified

Numerade educator

Question 1 The temperature field in a continuum is given by the expression [ heta=frac{e^{-3 t}}{x^{2}}, ] where ( x^{2}=x_{1}^{2}+x_{2}^{2}+x_{3}^{2} ). The velocity field of the medium has componets [ v_{1}=x_{2}+2 x_{3}, v_{2}=x_{3}-x_{1}, v_{3}=x_{1}+3 x_{2} . ] Determine the material derivative ( D heta / D t ) of the temperature field. Question 2 Determine the streamline and pathline equations for a two-dimensional flow in ( x-y ) plane with a velocity field of [ u=x(t+2), quad v=frac{y}{t+1} . ] The streamline and pathline pass the point ( M(1,1) ) at ( t=0 ). Question 3 The velocity potential for a given two dimensional flow field is [ phi=left(frac{5}{3} ight) x^{3}-5 x y^{2} . ] Show that the continuity equation is satisfied and determine the corresponding stream functions.

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ANSWERED

Rahul Kumar verified

Numerade educator

Question 1 The temperature field in a continuum is given by the expression [ heta=frac{e^{-3 t}}{x^{2}}, ] where ( x^{2}=x_{1}^{2}+x_{2}^{2}+x_{3}^{2} ). The velocity field of the medium has componets [ v_{1}=x_{2}+2 x_{3}, v_{2}=x_{3}-x_{1}, v_{3}=x_{1}+3 x_{2} . ] Determine the material derivative ( D heta / D t ) of the temperature field. Question 2 Determine the streamline and pathline equations for a two-dimensional flow in ( x-y ) plane with a velocity field of [ u=x(t+2), quad v=frac{y}{t+1} . ] The streamline and pathline pass the point ( M(1,1) ) at ( t=0 ). Question 3 The velocity potential for a given two dimensional flow field is [ phi=left(frac{5}{3} ight) x^{3}-5 x y^{2} . ] Show that the continuity equation is satisfied and determine the corresponding stream functions.

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