Sustainable Energy
2nd Edition
ISBN: 9781337551663
Author: DUNLAP, Richard A.
Publisher: Cengage,
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3. A steel bolt through a 31-in long aluminum tube has the nut turned on until it just touches the end of the tube. No stress is introduced on the bolt or the tube. The temperature of the assembly is raised from 70 to 81 degrees Fahrenheit. The cross-sectional area of the bolt is 0.09 sq. inch and the cross-sectional area of the tube of 0.30 sq. inch.
a. Find the thermal deformation (in inches) of the steel bolt. (Write your answer to 6-decimal places.)
b. Find the thermal deformation (in inches) of the aluminum tube. (Write your answer to 6-decimal places.)
c. Find the stress (in psi) induced in the steel bolt by the temperature change.
d. Find the stress (in psi) induced in the aluminum tube by the temperature change.
The block shown is made of a magnesium alloy for which E = 45 GPa and ν = 0.35. Knowing that σx = -180 MPa, determine (a) the magnitude of σy for which the change in the height of the block will be zero, (b) the corresponding change in the area of the face ABCD, (c) the corresponding change in the volume of the block.
Determine the thermal resistance R′ and the R-value for the glass window ofThe thermal resistance R′ and the R-value of the window can be determined from as shown , respectively.
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- Q8: Consider a steel rod of fixed ends. If the temperature of the rod is increased by AT-80 °C, then the generated thermal stress (in MPa) in the rod is: (Hint: For the steel, the Young's modulus (Y) is 2x10 N/m and the coefficient of linear thermal expansion (a) is 11 x 106 ly a) 2.2 b) 176.0 c) 352 d) 776.6arrow_forwardA rectangular nylon [E = 8 GPa; ?= 0.35; ? = 24 ×10 6/°C] plate has a circular hole in its center. At an initial temperature of T¡ = 15°C, the plate width is b = 260 mm, the plate height is h = 160 mm, the diameter of the central hole is d = 45 mm, and the thickness of the plate is t = 17 mm. At a final temperature of Tf= 52°C, determine (a) the diameter d of the central hole. (b) the thickness t of the plate. b harrow_forwardA 13 in length of aluminum tubing (with E = 11.4 x 106 psi and = 12 x 10-6 /deg F) having a cross-sectional area of 1.6 in2 is installed with “fixed” ends so that it is stress-free at 70 deg F. In operation, the tube is heated throughout to a uniform 500 deg F. Careful measurement at the higher temperature indicates that the fixed ends separate to 13.008 in. What loads are exerted on the ends of the tube, and what are the resultant stresses?arrow_forward
- A spherical stainless-steel tank having an inner diameter ‘D’, is used to store naturalgas at a pressure of ‘p’. The properties of the steel are as follows: yield stress in tensionis ‘T’; yield stress in shear is ‘S’ and modulus of elasticity is ‘E’. The desired factor ofsafety with respect to yielding is ‘F.S’.Determine the minimum permissible thickness t min of the tank. (D (mm)=620)( p (MPa)=25)( T (MPa)=1000)( S (MPa)=440)( E (GPa)=208)( F.S=3.4)arrow_forwardAn aluminum pipe has a length of 53 m at a temperature of 7°C. An adjacent steel pipe at the same temperature is 7 mm longer. At what temperature will the aluminum pipe be 21 mm longer than the steel pipe? Assume that the coefficient of thermal expansion for the aluminum is 22.5x10-6/°C and that the coefficient of thermal expansion for the steel is 12.5×106/°C. Answer: Tf = i °Carrow_forwardThe block shown is made of a magnesium alloy for which E=X2GPaand ϑ=0.35. Knowing that σx= X1 MPa, determine (a) the magnitude of σyfor which the change in the height of the block will be zero, (b) the corresponding change in the area of the face ABCD, (c) the corresponding change in the volume of the block.arrow_forward
- An aluminum pipe has a length of 64 m at a temperature of 15°C. An adjacent steel pipe at the same temperature is 2 mm longer. At what temperature will the aluminum pipe be 6 mm longer than the steel pipe? Assume that the coefficient of thermal expansion for the aluminum is 22.5x10-6/°C and that the coefficient of thermal expansion for the steel is 12.5x10-6/°C. Answer: T₁= i °℃arrow_forwardA rectangular nylon [E =8 GPa; v=0.35; a= 23×106/°C] plate has a circular hole in its center. At an initial temperature of T₁ = 22°C, the plate widthis b=310 mm, the plate height is h = 220 mm, the diameter of the central holeis d = 60 mm, and the thickness of the plateist= 18 mm. At a final temperature of T= 59°C, determine (a) the diameter d of the central hole. (b) the thickness t of the plate. Answers: (a) d = i (b) t= i b d mm mmarrow_forwardAn aluminum pipe has a length of 50 m at a temperature of 6°C. An adjacent steel pipe at the same temperature is 4 mm longer. At what temperature will the aluminum pipe be 12 mm longer than the steel pipe? Assume that the coefficient of thermal expansion for the aluminum is 22.5x106/°C and that the coefficient of thermal expansion for the steel is 12.5x10-6/°C. Answer: Tf = i °℃arrow_forward
- A capillary tube of diameter 2 mm is placed in a reservoir of water, and a similar capillary tube is placed in a reservoir of methanol. If both tubes are made of clean glass and the water-glass and methanol-glass contact angles are both approximately equal to 0°. Surface tension of water is 0.073 N/m. Surface tension and density of methanol are 0.0225 N/m and 791 kg/m3, respectively. 8.0 Determine the rise of methanol. a.) 7.4 mm b.) 5.8 mm c.) 14.9 mm d.) 2.9 mm e.) 9.0 Determine the rise of water. a.) 7.4 mm b.) 5.8 mm c.) 14.9 mm d.) 2.9 mm e.).arrow_forwardA high-density polyethylene [E = 135 ksi and a = 69 x 10-6/°F) block (1) is positioned in a fixture. The block is 2.1 in, by 2.2 in. by 36 in. long. At room temperature, a gap of 0.1 in. exists between the block and the rigid support at B. Assume L₁- 36 in and A = 0.1 in. Determine: (a) the normal stressa in block (1) caused by a temperature increase of 70°F. (b) the normal strain e in block (1) at the increased temperature. Answers: (a) a = (b) = i B 277.05 A LA psi. pc.arrow_forward1. When the force of 3 mN is applied to the plate the line AB in the liquid remains straight and has a velocity of 0.6x10-3 m/s. If the surface area of the plate in contact with the liquid is 0.6 m2, determine the approximate viscosity of the liquid. В B' 3 mN 4 mm Aarrow_forward
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