A spherical soap bubble has an inside radius R, a film thickness t, and a surface tension  σ. Derive a formula for the pressure within the bubble relative to the outside atmospheric  pressure. What is the pressure difference for a bubble with a 4 mm radius? Assume σ is the  same as for pure water. show solution and diagram if possibke

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As shown in Figure 2.1, liquid of density pis trapped by a gate ABC of unit width into the plane of the page. The gate is hinged at C, and consists of a vertical section AB of length H and an inclined section BC also of length H inclined at an angle with respect to the horizontal. Obtain an expression for the force P required to hold the gate in position. Neglect the weight of the gate and friction in the hinge. Some geometric properties of a rectangle are provided in Figure 2.2, where the symbols have their usual meanings. |6|2 b y + X C Figure 2.1 b N|O 2 Rectangle H H P a Area A = ba 2 C: Centroid a 1xx,c= |yy,c= 1 12 1 12 ·ba³ ab³