Water is circulating through a closed system of pipes in a two floor apartment. On the first floor, the water has a gauge pressure of 3.30 1

Question

Water is circulating through a closed system of pipes in a two floor apartment. On the first floor, the water has a gauge pressure of 3.30 105 Pa and a speed of 2.0 m/s. However, on the second floor, which is 4.4 m higher, the speed of the water is 3.5 m/s. The speeds are different because the pipe diameters are different. What is the gauge pressure of the water on the second floor

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Bơ 3 years 2021-08-21T13:37:10+00:00 2 Answers 4 views 0

Answers ( )

  1. thaiduong
    0
    2021-08-21T13:38:13+00:00
    Reply

    Answer:

    P₂ = 2.82755 * 10⁵ Pa

    Explanation:

    Parameters for the first floor:

    Guage pressure, P₁ = 3.30 * 10⁵ Pa

    Speed, v₁ = 2.0 m/s

    Height of the first floor = h₁

    Parameters of the second floor:

    Guage Pressure, P₂ = ?

    Speed = 3.5 m/s

    height of the second floor = h₂

    From the question, h₂ – h₁ = 4.4 m, i.e. h₁ – h₂ = – 4.4 m

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

    According to the Bernoulli’s equation

    P_{1} + 0.5 \rho (v_{1}) ^{2} + \rho g h_{1} = P_{2} + 0.5 \rho (v_{2}) ^{2} + \rho g h_{2}\\

    P_{2} = P_{1} + 0.5 \rho((v_{1}) ^{2} - (v_{2} )^{2}) + \rho g(h_{1} - h_{2) \\

    P_{2} = 3.30 * 10^{5} + 0.5*1000(2.0^{2} - 3.5^{2} ) + 1000*9.8(-4.4) \\P_{2} = 330000 - 4125 - 43120 \\P_{2} = 282755 Pa

    P_{2} = 2.82755 * 10^{5} Pa

  2. Adela
    0
    2021-08-21T13:38:58+00:00
    Reply

    Answer:

    P_{2} = 3.27*10^5 Pa

    Explanation:

    Given Data

    P_{1} = 3.8 * 10^5 Pa

    V_{1} = 1.8 m/s

    V_{2} = 4.6 m/s

    height of the second floor=h_{2}=4.5 m

    solution:

    For this type of numericals we use Bernoulli’s Equation which states as;  

    P_{1} +\frac{1}{2}pV_{1} ^{2} + pgh_{1} = P_{2} + \frac{1}{2} pV_{2} ^{2} + pg h_{2}

    we know that p=1.00*10^{3}kg/m^{3}

    and

    putting these values, we get

    3.8 * 10^5 +\frac{1}{2} (1000)1.8^{2} + 0 = P2 +\frac{1}{2} (1000) 4.6^{2} + (1000) (9.8)(4.5)

    using calculator, we get

    P_{2} = 3.27*10^5 Pa

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