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GATE Mechanical Engineering (ME) 2023 Shift 1 Solved Paper

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Question : 63

Total: 65

Consider a unidirectional fluid flow with the velocity field given by
V(𝑥, 𝑦, 𝑧, 𝑡) = 𝑢(𝑥, 𝑡) 𝑖̂
where 𝑢(0,𝑡) = 1. If the spatially homogeneous density field varies with time 𝑡 as
𝜌(𝑡) = 1 + 0.2𝑒^−𝑡
the value of 𝑢(2, 1) is ______________. (Rounded off to two decimal places) Assume all quantities to be dimensionless.

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