Question

A horizontal pipe carries a smoothly flowing liquid of density of 1330 kg/m3. At Locations 1 and 2 along the pipe, the diameters are ?1=5.71 cm and ?2=2.33 cm, respectively. The flow speed at Location 1 is 2.07 m/s . What is the pressure difference Δ? between Location 2 and Location 1 (including its sign)? Ignore viscosity.

Answer #1

Density of fluid =
= 1330 kg/m^{3}

Pressure at location 1 = P_{1}

Pressure at location 2 = P_{2}

Diameter of pipe at location 1 = d_{1} = 5.71 cm =
0.0571 m

Diameter of pipe at location 2 = d_{2} = 2.33 cm =
0.0233 m

Speed of flow at location 1 = V_{1} = 2.07 m/s

Speed of flow at location 2 = V_{2}

Pressure difference between location 2 and 1 =
P = P_{2} - P_{1}

Area of pipe at location 1 = A_{1} =
d_{1}^{2}/4

Area of pipe at location 2 = A_{2} =
d_{2}^{2}/4

By continuity equation,

A_{1}V_{1} = A_{2}V_{2}

(d_{1}^{2}/4)V_{1}
= (d_{2}^{2}/4)V_{2}

V_{1}d_{1}^{2} =
V_{2}d_{2}^{2}

(2.07)(0.0571)^{2} =
V_{2}(0.0233)^{2}

V_{2} = 12.43 m/s

The pipe is horizontal, hence there is no height difference between locations 1 and 2.

By bernoulli's equation,

P_{1} +
V_{1}^{2}/2 = P_{2} +
V_{2}^{2}/2

P_{2} - P_{1} =
(V_{1}^{2} - V_{2}^{2})/2

P
= (1330)[(2.07)^{2} - (12.43)^{2}]/2

P = - 99896.3 Pa

Pressure difference between location 2 and location 1 = - 99896.3 Pa

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