1.) A block of birch wood floats in oil with 82.6% of its volume submerged. What

Question

1.) A block of birch wood floats in oil with 82.6% of its volume submerged. What is the density of the oil? The density of the birch is 0.69 g/cm3.

2.) Water entering a house flows with a speed of 0.25 m/s through a pipe of 1.3 cm inside radius. What is the speed of the water at a point where the pipe tapers to a radius of 2.4 mm?

3.) Suppose air, with a density of 1.29 kg/m3 is flowing into a Venturi meter. The narrow section of the pipe at point A has a diameter that is 1/3 of the diameter of the larger section of the pipe at point B. The U shaped tube is filled with water and the difference in height between the two sections of pipe is 1.65 cm. How fast is the air moving at point B?

Explanation / Answer

3) Use the Bernoulli equation and the equation of constant volume flow. The equation states that 1/2 ? v2 + P + ?gH = constant As we are at a the same height, we can neglect the H part. So, we have 1/2?v2 + P = constant Using the equation of continuity, we have Velocity at A * Cross-section of A = Velocity at B * Cross section at B So we have Velocity at A = 9 * Velocity at B (As the diameter is 1/3 times, the cross section is 1/9 times) Let the velocity at B be x. Now apply the derived Bernoulli equation. (A) (B) 1/2? (9v)2 = 1/2 ? (v)2 + P 1/2 ? (80) v2 = P 40 ? v2 = P P is the pressure difference as shown by the Venturi meter. This is equal to ? * h * g = 1000 * 1.65*10^-2 * 9.8 = 161.7 So, 40 * 1.29 * v *v = 161.7 v*v = 3.0197 v = 1.770 m/s vB = 1.77 m/s ---> Answer

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