A bar of length 2 m is fully insulated along its sides. It is initially at a uniform temperature of 10C and at t = 0 the ends are plunged into ice and maintained at a temperature of OC. Determine an expression for the temperature at a point
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- Which spring, the truncated cone spring or the helical spring, would have a larger spring constant? Explain.The open-ended pipe has a wall thickness of 2mm and an internal diameter of38mm. Calculate the pressure that the ice exerts on the interior wall of the pipe tocause it to burst along the cross-section and along the longitudinal section. Allowablestress at freezing temperature of the material is 350MPaA cylinder has an internal diameter of 230 mm, has walls 5 mm thick and is 1 m long. It is found to change in internal volume by 12.0 x 10-6 m3 when filled with a liquid at a pressure p. If E = 200GN/m2 and v = 0.25, and assuming rigid end plates, determine the values of hoop stress
- A water tank is completely filled with liquid water at 60°C. The tank material is suchthat it can withstand tension caused by a volume expansion of 4%. Determine the maximum temperature rise allowed without jeopardizing safety. Take water coefficient of expansion (β) as 5.22 x 10-4 1/K at this temperature.1. A steel sphere 3” in diameter heated to 600oF, is to be cooled by immersion in an oil bath at 100oF. Calculate the average temperature of the sphere a) 10 sec and b) 6 min after immersion. For steel, k = 26Btu/ft-h-oF; = 486lb/ft3 ; Cp = 0.11Btu/lboF.A cylindrical pressure vessel has an inner diameter of 1.2 m and a thickness of 12mm. Determine the maximum internal pressure it can sustain so that neither itscircumferential nor its longitudinal stress component exceeds 140 MPa. Under thesame conditions, what is the maximum internal pressure that a spherical vessel with a similar inner diameter can sustain?
- Awatermelon initially at 35°C is to be caoled by dropping itinto a lake at 15°C. After 4 h and 40 min of cooling the center temperature of watermelon is measured to be 20°C. Treating the watermelon 25 a 20-c-diameter sphere and using the properties k = 0.618 WimA chromel–constantan thermocouple measuring the temperature of a fluid is connected by mistake with copper–constantan extension leads (such that the two constantan wires are connected together and the copper extension lead wire is connected to the chromel thermocouple wire). If the fluid temperature was actually 250 C and the junction between the thermocouple and extension leads was at 90 C, what e.m.f. would be measured at the open ends of the extension leads if the reference junction is maintained at 0 C? What fluid temperature would be deduced from this (assuming that the connection error was not known)?A thermometer is being designed for a process in which the temperature varies from 0 to 180 °C; from experience it is known that the process temperature, when it gets out of control, reaches up to 240 ° C. Considering that only the bulb is in contact with the part inside the equipment, what should be the volume of the safety vial? It is known that the bulb has a length of 1.2 cm and a diameter of 0.5 cm; the capillary has a length of 20 cm and the scale of the thermometer is -10 to 190 ° C. Consider that the coefficient of volumetric expansion for mercury is 1.82×10−4 ° C− 1
- A water tank is completely filled with liquid water at 20°C. The tank material is such that it can withstand tension caused by a volume expansion of 0.8 percent. Determine the maximum temperature rise allowed without jeopardizing safety. For simplicity, assume ? = constant = ? at 40°C.A metallic ball of radius ro = 5 mm, is initially in equilibrium at 400 C in a furnace. It is suddenly dropped to water at 20 C ( hw = 11003 W/m^2). The properties of the sphere are density= 3000 kg/m3, k = 20 W/m_ K, c = 1000 J/kg K, and α= 6.66E-6 m2/s. Calculate the time required for the center of the sphere to cool to 50 C.14. A commonly used method of fastening one part to another part iscalled “shrink fi tting.” A steel rod has a diameter of 2.0026 cm, and afl at plate contains a hole whose diameter is 2.0000 cm. The rod is cooledso that it just fi ts into the hole. When the rod warms up, the enormousthermal stress exerted by the plate holds the rod securely to the plate. Byhow many Celsius degrees should the rod be cooled?