Compute the Jacobian Matrix of the following :[ x ; = [ L1q1 + L2cos(q2) + L3cos(q2+q3) ;y ; L2sin(q2) + L3sin(q2+q3) ;z ] -L2cos(q2) - L3sin(q2 + q3) ]

Consider a large isothermal enclosure that is maintained at a uniform temperature of 2000 k. calculate the emissive power of the radiation that emerges from a small aperture on the enclosure surface. what is the wavelength ? , below which 10% of the emission is concentrated? what is the wavelength ? 2 above which 10% of the emission is concentrated? determine the wavelength at which maximum spectral emissive power occurs. what is the irradiation incident on a small object placed inside the enclosure?

A2-m rigid tank initially contains saturated water vapor at 100 kpa. the tank is connected to a supply line through a valve. steam is flowing in the supply line at 600 kpa and 300 c. the valve is opened, and steam is allowed to enter the tank until the pressure in the tank reaches the line pressure, at which point the valve is closed. a thermometer placed in the tank indicates that the temperature at the final state is 200°c. determine (a) the mass of steam that has entered the tank (b) the amount of heat transfer.

Amixture of slurry and mud is to be pumped through a horizontal pipe of diameter 500 mm. the fluid behaves as a bingham plastic with a yield stress of 30 pa and viscosity 0.04 pa.s. describe the effects of the shear stress through a transverse section of the pipe by plotting the variation in shear stress and velocity profile: (i) just before the slurry starts to move (ii) as the slurry flows when the pressure gradient is double that in part (i)