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AleksandrR [38]
3 years ago
6

Oil (SAE 30) at 15.6 oC flows steadily between fixed, horizontal, parallel plates. The pressure drop per unit length along the c

hannel is 35 kPa/m, and the distance between the plates is 9 mm. The flow is laminar. Determine: (a) the volume rate of flow (per meter of width), (b) the magnitude of the shearing stress acting on the bottom plate, and (c) the velocity along the centerline of the channel.
Engineering
1 answer:
Nitella [24]3 years ago
7 0

Answer:

(a) The volume rate of flow per meter width = 5.6*10⁻³ m²/s

(b) The shear stress  acting on the bottom plate = 157.5 N/m²

(c) The velocity along the centerline of the channel = 0.93 m/s

Explanation:

(a)

Calculating the distance of plate from centre line using the formula;

h = d/2

where h = distance of plate

d = diameter of flow = 9 mm

Substituting, we have;

h = 9/2

  = 4.5 mm = 4.5*10^-3 m

Calculating the volume flow rate using the formula;

Q = (2h³/3μ)* (Δp/L)

Where;

Q = volume flow rate

h = distance of plate = 4.5*10^-3 m

μ = dynamic viscosity = 0.38 N.s/m²

(Δp/L) = Pressure drop per unit length = 35 kPa/m = 35000 Pa

Substituting into the equation, we have;

Q = (2*0.0045³/3*0.38) *(35000)

    = (1.8225*10⁻⁷/1.14) * (35000)

    = 1.60*10⁻⁷ * 35000

   = 5.6*10⁻³ m²/s

Therefore, the volume flow rate = 5.6*10⁻³ m³/s

(b) Calculating the shear stress acting at the bottom plate using the formula;

τ  = h*(Δp/L)

    = 0.0045* 35000

    = 157.5 N/m²

(c) Calculating the velocity along the centre of the channel using the formula;

u(max) = h²/2μ)* (Δp/L)

   = (0.0045²/2*0.38) * 35000

   =2.664*10⁻⁵ *35000

   = 0.93 m/s

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<u>ARPANET is the direct precedent for the Internet, a network that became operational in October 1969 after several years of planning. </u>

Its promoter was DARPA (Defense Advanced Research Projects Agency), a US government agency, dependent on the Department of Defense of that country, which still exists.

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<em><u> Below I present as a summary some of the most relevant aspects exposed on the requested website about the origin and authors of ARPANET:</u></em>

<em><u></u></em>

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