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The figure below shows how water is drawn from a large tank into a low-lying container using a rubber tube of uniform cross-sectional area 0.002 ext m2. Determine the force driving out the water.

Physics

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Answer

19.6 N\text{19.6 N}

Step-by-step solution

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here is the solution to question 4.

4. The figure below shows how water is drawn from a large tank into a low-lying container using a rubber tube of uniform cross-sectional area 0.002 m20.002 \text{ m}^2. Determine the force driving out the water.

  1. Identify the effective height difference.

    The force driving the water out is due to the pressure difference created by the vertical height difference between the water surface in the large tank and the outlet of the tube.
    From the diagram:
    Height of water surface from the top of the tube = 50 cm50 \text{ cm}
    Height of the outlet from the top of the tube = 150 cm150 \text{ cm}
    Effective height difference h=150 cm−50 cm=100 cmh = 150 \text{ cm} - 50 \text{ cm} = 100 \text{ cm}.

  2. Convert the height to meters.

    h=100 cm=1.0 mh = 100 \text{ cm} = 1.0 \text{ m}
  3. State the given values.

    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} (standard value)
    Cross-sectional area A=0.002 m2A = 0.002 \text{ m}^2

  4. Calculate the pressure difference.

    The pressure difference ΔP\Delta P is given by the formula P=ρghP = \rho g h:

    ΔP=(1000 kg/m3)×(9.8 N/kg)×(1.0 m)\Delta P = (1000 \text{ kg/m}^3) \times (9.8 \text{ N/kg}) \times (1.0 \text{ m}) ΔP=9800 Pa\Delta P = 9800 \text{ Pa}
  5. Calculate the force driving out the water.

    The force FF is the pressure difference multiplied by the cross-sectional area:

    F=ΔP×AF = \Delta P \times A F=(9800 Pa)×(0.002 m2)F = (9800 \text{ Pa}) \times (0.002 \text{ m}^2) F=19.6 NF = 19.6 \text{ N}

    The force driving out the water is 19.6 N\text{19.6 N}.

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