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The figure below shows a water U-tube manometer used to measure the gas pressure of a gas supply. Calculate the gauge pressure of the gas.

Physics

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Answer

882 Pa\text{882 Pa}

Step-by-step solution

4 steps

Here is the solution to the question.

10. The figure below shows a water U-tube manometer used to measure the gas pressure of a gas supply.

  1. Identify the height difference in the manometer.

    From the figure, the difference in the water levels between the two arms is 9 cm9 \text{ cm}.

    h=9 cmh = 9 \text{ cm}

  2. Convert the height difference to meters.

    h=9 cm=0.09 mh = 9 \text{ cm} = 0.09 \text{ m}

  3. State the known values for water and gravitational field strength.

    Density of water ρ=1000 kg/m3\rho = 1000 \text{ kg/m}^3
    Gravitational field strength g=9.8 N/kgg = 9.8 \text{ N/kg}

  4. Calculate the gauge pressure of the gas.

    The gauge pressure of the gas is equal to the pressure exerted by the column of water of height hh.

    P=ρghP = \rho g h P=(1000 kg/m3)×(9.8 N/kg)×(0.09 m)P = (1000 \text{ kg/m}^3) \times (9.8 \text{ N/kg}) \times (0.09 \text{ m}) P=9800 Pa/m×0.09 mP = 9800 \text{ Pa/m} \times 0.09 \text{ m} P=882 PaP = 882 \text{ Pa}

    The gauge pressure of the gas is 882 Pa\text{882 Pa}.

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