Physics College

A flat plate with surface area of 1.8 m2m2 is sliding on a horizontal table with 3.7 mmmm thick oil layer on top. Force applied on the plate in the direction of movement is 2.2 NN. Dynamic viscosity of the oil is 0.89 x10-³ Ns/m².​

Answers

Answer 1

The velocity gradient across the 3.7 mm thick oil layer on the flat plate sliding on the horizontal table is 0.594 m/s/m.

Given:

Surface area of the plate (A) = 1.8 m^2

Thickness of the oil layer (h) = 3.7 mm = 0.0037 m

Force applied on the plate (F) = 2.2 N

Dynamic viscosity of the oil (η) = 0.89 x 10^-3 Ns/m^2

To calculate the velocity gradient across the oil layer, we can use the equation:

τ = η * du/dy

where τ is the shear stress, η is the dynamic viscosity, and du/dy is the velocity gradient.

Since the force (F) applied on the plate is responsible for the shear stress, we can write:

τ = F / A

Substituting the given values, we have:

F / A = η * du/dy

Solving for du/dy, we get:

du/dy = (F / A) / η

Substituting the values, we have:

du/dy = (2.2 N) / (1.8 m^2 * 0.89 x 10^-3 Ns/m^2)

du/dy = 0.594 m/s/m

Therefore, the velocity gradient across the oil layer is 0.594 m/s/m.

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Related Questions

Usually, we do a
when a population is hard to study, for some reason.

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Usually, we use sampling when a population is hard to study, for some reason.

Sampling is a technique commonly employed in research and statistics when it is impractical or impossible to study an entire population directly. It involves selecting a subset, or sample, from the population and using the information gathered from the sample to make inferences about the entire population. This is done with the assumption that the sample is representative of the population and that the findings from the sample can be generalized to the larger population.

There are several reasons why a population might be difficult to study comprehensively. One reason is the size of the population. For example, if the population of interest is the entire world or a country, it would be practically impossible to study each individual in the population due to logistical constraints and limited resources. In such cases, sampling allows researchers to gather information from a smaller, manageable subset of the population.

Another reason for using sampling is when the population is dispersed or geographically scattered. If the population is spread out across a wide area, it can be challenging and costly to reach and collect data from every individual. Sampling allows researchers to select representative individuals or clusters from different regions, making data collection more feasible.

Additionally, there are cases where the population is inaccessible or hard to reach due to privacy concerns or ethical considerations. For example, if the population consists of individuals with certain medical conditions or sensitive personal information, it may be challenging to obtain consent or access to the entire population. In such cases, researchers can use sampling methods to obtain data from a subset of individuals who are willing to participate and meet the necessary criteria.

In summary, sampling is a valuable tool when studying populations that are hard to access, too large, or dispersed. It allows researchers to gather relevant data from a representative subset of the population and make valid inferences about the larger population, despite the challenges posed by studying the population as a whole.

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Usually, we use                  when a population is hard to study, for some reason.

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