QUIZ 11

1. A 2-kg aluminum ball (SG = 2.7) is completely submerged in alcohol (SG = 0.8). What is the buoyant force the aluminum ball exerted? Take the density of water as 10³ kg/m³.

Solution. We find the volume of the ball from

               V = m_Al /r_Al = m_Al/SG_Al r_water = (2kg)/(2.7)(10³kg/m³)

                   = 7.4 x 10^-5m³.

    We find the buoyant force from

               F_B = r_alcohol Vg = SG_alcohol r_waterVg 

                    = (0.8)(10³kg/m³)(7.4 x 10^-5m³)(9.80m/s³)

                    = 5.8N.

2. Water is flowing at 3m/s in a horizontal pipe under a pressure of 200kpa. The pipe narrows to half its original diameter.  What is the pressure in the narrow section?

Solution. 

 We find the speed at he narrow part from

             A₁v₁ = A₂v₂;

             v₂ = 4v₁ = 12m/s.

From Bernoulli's equation we have

             P₁ + 1/2rv₁² + rgh₁ =  P₂ + 1/2rv₂² + rgh₂;

As h₁ = h₁, we have

             200kpa + 1/2(10³ kg/m³)(3m/s)² = P₂ + 1/2(12m/s)²

which gives P₂ = 132.5kpa.