Calculus and analytical(2)

CALCULUS AND ANALYTICAL GEOMETRY

(NS) IMTIAZ ALI SHAUKAT

6352

DE-35,MECHANICAL ENGINEERING -B

PRESENTATION TOPIC

REVOLUTION SPACE REQUIRED FOR TURBINES AND CAR AXLE

SPACE REQUIRED THE SPACE REQUIRED FOR

REVOLTION OF TURBINE BLADE CAN BE DETERMINED FROM THE VOLUME OCCUPIED BY THE BLADE DURING ITS REVOLUTION.

BASIC CONCEPT FOR CALCULATING VOLUME

We rotate THE GIVEN CURVE about a given axis to get the surface of the solid of revolution.  For purposes of this discussion let’s rotate the CURVE about a line. Doing this for the curve above gives the following three dimensional region.

FORMULAE 

First, the inner radius is NOT  x.  The distance from the x-axis to the inner edge of the ring is x, but we want the radius and that is the distance from the axis of rotation to the inner edge of the ring.  So, we know that the distance from the axis of rotation to the x-axis is 4 and the distance from the x-axis to the inner ring is x.  INNER RADIUS: 4-X 

CALCULATING VOLUME

outer radius is

Putting values in this formula we can get volume.

STREAM GENERATOR

GEOMETRY OF BLADES OF TURBINE

blade of turbine is shown in figure

WIND MILL TURBINE

TURBINES

A turbine is a rotary mechanical device that extracts energy from a fluid flow and converts it into useful work. A turbine is a turbo-machine with at least one moving part called a rotor assembly, which is a shaft or drum with blades attached. Moving fluid acts on the blades so that they move and impart rotational energy to the rotor.

GEOMETRY OF WIND TURBINE BLADES

VOLUME FOR REVOLVING A BLADE OF TURBINE

The volume occupied by revolving this blade is actually the space for turbine revolution.

The geometry of the blade shown in figure .now we assume that geometry as two functions overlapped and forming a region. We take one side of the blade as on function and other side as other function..

So the same FORMULAE would be followed….

SPACE OCCUPIED BY BLADE OF TURBINE

SO KNOWING THE OUTER AND INNER RADIUSWE CAN FINF AREA THEN VOLUME.SO BY PUTTING FORMULAE IN THIS WE CAN FIND THE VOLUME OCCUPIED BY THE REVOLUTION OF THAT BLADE

CAR AXLE

CAR AXLE

An axle is a central shaft for a rotating wheel or gear. On wheeled vehicles, the axle may be fixed to the wheels, rotating with them, or fixed to its surroundings, with the wheels rotating around the axle.

SPACE FOR REVOLVING CAR AXLE

The geometry of the CAR AXLE shown in figure .now we assume that geometry as two functions overlapped and forming a region. We take one side of the blade as on function and other side as other function..

So the same FORMULAE would be followed….

THANK YOU