or a sliding plate viscometer of the type we have discussed in class, it is found that when the distance between the plates is 2 mm, a shearing stress of 150 Pa develops at the upper plate when it is pulled at a velocity of 0.5 m/s. The viscosity of the Newtonian fluid between the plates is:
Question
or a sliding plate viscometer of the type we have discussed in class, it is found that when the distance between the plates is 2 mm, a shearing stress of 150 Pa develops at the upper plate when it is pulled at a velocity of 0.5 m/s. The viscosity of the Newtonian fluid between the plates is:
Solution 1
The viscosity of a Newtonian fluid can be calculated using the formula for shear stress:
τ = η * (du/dy)
where: τ is the shear stress, η is the dynamic viscosity, du/dy is the velocity gradient.
In this case, the shear stress τ is given as 150 Pa, the velocity du is 0.5 m/s, and the distance dy between the plates is 2 mm or 0.002 m.
Rearranging the formula to solve for viscosity gives:
η = τ / (du/dy)
Substituting the given values into the formula gives:
η = 150 Pa / (0.5 m/s / 0.002 m)
η = 150 Pa / 250 s⁻¹
η = 0.6 Pa.s
So, the viscosity of the Newtonian fluid between the plates is 0.6 Pa.s.
Solution 2
The viscosity of a Newtonian fluid can be calculated using the formula for shear stress:
τ = η * du/dy
where: τ is the shear stress, η is the dynamic viscosity, du/dy is the velocity gradient.
In this case, the shear stress τ is given as 150 Pa, the velocity du is 0.5 m/s, and the distance dy is 2 mm or 0.002 m.
Rearranging the formula to solve for viscosity gives:
η = τ / (du/dy)
Substituting the given values into this equation gives:
η = 150 Pa / (0.5 m/s / 0.002 m)
η = 150 Pa / 250 s⁻¹
η = 0.6 Pa.s
So, the viscosity of the Newtonian fluid between the plates is 0.6 Pa.s.
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