explain the relation between pressure graidient to isobars,wind direction & velocity

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Pressure gradient is the amount of change in atmosphere pressure between 2 points & is depicted on the synoptic chart by the differential spacing of isobars(imaginary lines joining points on the map with equal barometric pressure)-a wide spacing indicates weak or gentle gradient (& therefore wind of low velocity) while narrow spacing indicates a steep gradient (& therefore winds of high velocity).Thus, when the wind is subjected to greater pressure on one side than on the other, this imbalance produces a net imbalanced force from a region of high pressure to the region of low pressure called the Pressure Gradient Force.
                    Pressure gradient force=1/density of atmosphere*(rate of pressure change*over distance 'P' )/(rate of pressure change* in the direction 'X' )
This pressure difference between the two isobars cause the wind to blow as per Newton's second law f motion & if these differences are high wind velocity is high & if this difference is low wind velocity is low. the isobars are curved & the wind blowing along the isobars is called Geostrophic wind, where the actual speed departs more from geostrophic than in regions where isobars are straight lines, resulting in geostrophic imbalance. Around the highs in northern hemisphere wind is clockwise parallel to isobars & horizontal pressure gradient force is directed radially outwards away from the centre of high & Coriolis effect directed inwards & changing horizontal pressure gradient force help in conservation of angular momentum resulting in increased wind velocity.
                                  Around low, horizontal pressure gradient force is inwardly & Coriolis force moves radially outwards & horizontal pressure gradient force > Coriolis force & wind blows parallel to isobars but anticlockwise & since the air movement is equatorwards therefore angular momentum is not maintained & wind velocity is low i.e., sub-geostrophic. In the southern hemispheres all these motions are reversed. therefore,If the winds move polewards across isobars then by the virtue of the Law of Conservation of Angular Momentum it's velocity increases in both the hemispheres. 

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