A pressurizes vessel is filled with helium. It is very important that the pressu

Question

A pressurizes vessel is filled with helium. It is very important that the pressure in the tank is carefully measured every hour. You are designing a titled manometer to make these readings. The fluid in the manometer is water (p= 1000 kg/m^3). You would like the sensitivity of the pressure measuring device to be such that a change of pressure in the helium tank of 80 Pa will result in a change in the manometer reading of 1 cm. Assume that the diameter of reservoir A is sufficiently larger than the diameter of the manometer tube to allow us to assume that height h= 10 cm remains constant.

a) What angle does the manometer tube need to be at to achieve the desired sensitivity?

b) If the maximum pressure expected in the tank is 200 kPa how long does the manometer tube need to be?

c) Is your answer in (b) practical, why ?

Explanation / Answer

Density of water, rho = 1000 kg/m^3

Slant height = h = 1 cm = 0.01 m

Vertical height = h*sin theta

Pressure difference = rho*g*h*sin theta

80 = 1000*9.81*0.01*sin theta

Solving, theta = 54.6 deg

b)

200*10^3 = 1000*9.81*h*sin54.6

h = 25 m

c)

25 m is very long. If we use the manometric fluid as merucry which has higher density than water, the tube length can be reduced.

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