The velocity of a lubricant between two solid surfaces separated by a distance h is given...

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The velocity of a lubricant between two solid surfaces separated by a distance h is given by the function u(y) = Gy² + Ay+B, where G is a constant pressure gradient and A and B are arbitrary constants. Given that u(0) = 0 and u(h)=V: (i) Show that u(y) = Gy(y-h)+Vy/h [3 marks] (ii) If G=-1, V=1 and h=3, calculate the maximum and average values of the velocity. [7 marks] dy v Solve+ = cost. dt t [5 marks] The blade of a plastic kitchen spatula has been designed to have a shape given by the curve x = 6y-y² between x=0 and x=9cm, as shown in Figure 2. The thickness of the blade is given by the function h(x, y) = a + bx where a = 0.3 cm and b=0.1. If the plastic has a uniform density of 0.92 g/cm³, calculate the mass of the blade. [10 marks] The velocity of a lubricant between two solid surfaces separated by a distance h is given by the function u(y) = Gy² + Ay+B, where G is a constant pressure gradient and A and B are arbitrary constants. Given that u(0) = 0 and u(h)=V: (i) Show that u(y) = Gy(y-h)+Vy/h [3 marks] (ii) If G=-1, V=1 and h=3, calculate the maximum and average values of the velocity. [7 marks] dy v Solve+ = cost. dt t [5 marks] The blade of a plastic kitchen spatula has been designed to have a shape given by the curve x = 6y-y² between x=0 and x=9cm, as shown in Figure 2. The thickness of the blade is given by the function h(x, y) = a + bx where a = 0.3 cm and b=0.1. If the plastic has a uniform density of 0.92 g/cm³, calculate the mass of the blade. [10 marks]