Question #154974

a) Write down the equation for the relationship between the shear stress and the shear rate for Newtonian fluid defining the variables and parameters used.

b) Oil with a density of 770 kg m^{−3} flows through a pipe with a diameter of 30 cm at a rate of 20,000 tonnes per day. Calculate the velocity of the oil in the pipe.

c) A liquid flows in a hosepipe of internal diameter 1.8 cm with a velocity of 150 cm s^{-1}. Calculate the velocity of the water in the nozzle at the end of the pipe which has a diameter of 0.75 cm.

d) Water at 20°C and 1 atm has a density = 998.0 kg/m3. Calculate the density at 35°C to 3 significant figures if the coefficient of volume

∆𝜌𝜌⁄𝜌𝜌

expansion of the water is given by 𝛽𝛽 = − = 0.337x10^{-3} K^{-1}.

∆𝑇𝑇

e) A brick wall with 0.1 m thickness (k = 0.7 W m^{−1}K^{−1}) is exposed to a cold wind at 270 K through a convection heat transfer coefficient of

40 W m^{−2}K^{−1}. On the other side is calm air at 330K, with a convection

heat transfer coefficient of 10 W m^{−2}K^{−1}. Calculate the rate of heat transfer per unit area (heat flux).

Expert's answer

a) **Shear rate** is the velocity **of** the moving plate divided by the distance **between** the plates. ... According **to** Newton's Law, **shear stress** is **viscosity** times **shear rate**. Therefore, the **viscosity** (eta) is **shear stress** divided by **shear rate**. Only Newtonian liquids can be described by this simple **relation**.

b) 20000 /0.77 = 25 974,026 L.

25 974,026/3600= 0.3 L/s.

c) 1.8 x 150/0.75= 360 cm/s.

d) 0.998 x 0.337 = 0,336326.

e) 20 .

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