A glass tube has several different cross-dectional areas with the values indicat

Question

A glass tube has several different cross-dectional 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 8.0m/s. Three points within the tube are labeled A, B, and C.

a) at what speed is mercury flowing past the point labeled A?

b) what is the total pressure at point A?

c) what is the total pressure at point B?

d) Determine the height h of mercury in the vertical tube with the evacuated upper end (meaning it is open to atmospheric pressure).

Explanation / Answer

given

vC = 8 m/s

a) use continuty equation

A_A*v_A = A_C*v_C

v_A = A_C*v_C/A_A

= 6*8/12

= 4 m/s <<<<<<<<-------------------Answer

b)

use Bernoulli's theorem

PA + 0.5*rho*V_A^2 = PC + 0.5*rho_v_C^2

PA = PC + 0.5*rho*(v_C^2 - v_A^2)

= 1.013*10^5 + 0.5*13.6*10^3*(8^2 - 4^2)

= 4.277*10^5 pa <<<<<<<<<<----------------Answer

c) use continuty equation

A_B*v_B = A_C*v_C

v_B = A_C*v_C/A_B

= 6*8/5.6

= 8.57 m/s

use Bernoulli's theorem

PB + 0.5*rho*V_B^2 = PC + 0.5*rho_v_C^2

PB = PC + 0.5*rho*(v_C^2 - v_B^2)

= 1.013*10^5 + 0.5*13.6*10^3*(8^2 - 8.57^2)

= 3.707*10^4 pa <<<<<<<<<<----------------Answer

d) we know, PB = rho*g*h

==> h = PB/(rho*g)

= 3.707*10^4/(13.6*10^3*9.8)

= 0.278 m <<<<<<<<<<----------------Answer

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