A glass tube has several different cross-sectional areas with the values indicated in the figure.A piston at the left end of the tube exerts pressure so that mercury within the tube flows from the right end with a speed of 8.0 m/s.Three points within the tube are labeled A,B,and C.
Notes: The drawing is not drawn to scale.
Atmospheric pressure is 1.01 × 10⁵ N/m²;and the density of mercury is 13 600 kg/m³.
-Determine the height h of mercury in the manometer with the evacuated upper end.
A)136 mm
B)269 mm
C)278 mm
D)366 mm
E)371 mm

Question

A glass tube has several different cross-sectional areas with the values indicated in the figure.A piston at the left end of the tube exerts pressure so that mercury within the tube flows from the right end with a speed of 8.0 m/s.Three points within the tube are labeled A,B,and C.
  Notes: The drawing is not drawn to scale.
Atmospheric pressure is 1.01 × 10⁵ N/m²;and the density of mercury is 13 600 kg/m³.
-Determine the height h of mercury in the manometer with the evacuated upper end.
A)136 mm 
B)269 mm 
C)278 mm 
D)366 mm 
E)371 mm

Quizplus · Accepted Answer

At point A, the pressure is atmospheric pressure plus the pressure due to the column of mercury of height h, density ρ and acceleration due to gravity g (p = P₀ + ρgh). At point B, the pressure is also atmospheric pressure plus the pressure due to the column of mercury of height h, density ρ and acceleration due to gravity g, plus the pressure due to the flow of mercury of speed v and density ρ/2 (p = P₀ + ρgh + (ρ/2)v²). At point C, the pressure is atmospheric pressure plus the pressure due to the column of mercury of height h/2, density ρ/2 and acceleration due to gravity g, plus the pressure due to the flow of mercury of speed v and density ρ/2 (p = P₀ + (ρ/2)(g+h/2) + (ρ/2)v²). Because the pressures at points A, B, and C are equal, we can equate the three equations and solve for h, which gives h = 278 mm. Therefore, the answer is C.

A Glass Tube Has Several Different Cross-Sectional Areas with the Values