Answer to Question #283142 in Physics for Kimgcash

Question

A glass U-tube of uniform cross-sectional area is sealed at one end.

The air in the tube is initially at IUPAC standard atmospheric

pressure (100 kPa) when water is poured into the tube sealing the

U-tube and compressing the gas trapped in the sealed end.

a) If the difference in the water levels between the two sides of

the tube is x = 50.0 cm, what is the pressure of the air in the

sealed end of the tube. The density of water is 1000 kgm-3.

b) If the length of the air in the sealed end of the tube is 20.0 cm,

what pressure would be required to reduce this to 5.00 cm?

What would the value of x be to apply this pressure?

Answer 1

(a) The pressure is

$$p=p_i+\rho_w gh=100+(1000·9.8·0.5)/10^3=\\=104.9\text{ kPa}.$$

(b) Assuming no temperature change:

$$p_f=100\dfrac{20}{5}=400\text{ kPa}.$$

$$h=\dfrac{p_f-p_i}{\rho_wg}=30.6\text{ m}.$$