A horizontal pipe carries a smoothly flowing liquid with density 1.39 times 103

Question

A horizontal pipe carries a smoothly flowing liquid with density 1.39 times 103 kg/m^3. At locations 1 and 2 along the pipe the diameters are 5.45 cm and 2.17 cm, respectively. Is the flow speed at location 2 higher or lower than at location 1? Can't tell from the data Lower Higher The flow speed at location 1 is 1.67 m/s. What is the pressure difference between location 2 and location 1 (including its sign)? Ignore viscosity. Is the pressure at location 2 higher or lower than at location 1? Higher Lower Can't tell

Explanation / Answer

A) Applying the equation of motion of fluid

A1 *V1 = A2 *V2

v2 / v1 = A1 /A2 = 2* pi * (5.45/2)^2 *10-4 / 2* pi * (2.17/2)^2 *10-4 = 5.45^2 / 2.17^2 = 29.70 / 4.71 = 6.31

v2 = 6.31 * v1 Hence the speed of flow at location 2 is higher than 1.

B) If v1 = 1.67 m/s then v2 = 6.31 * 1.67 = 10.54 m/s

P1 - P2 = 0.5 * rho * (v22 - v12)

= 0.5 * 1.39* 103 * ( 111.09 - 2.79) = 75.27 kPa

C) According to bernoullie's theorem, the area of location 2 is smaller than 1, hence the presssure at location 2 is higher than that of location 1.

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