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Question

The flow of water around the bridge pier is to be studied using a model built to a scale of $1 / 15$. If the river flows at $0.8 \mathrm{~m} / \mathrm{s}$, find the corresponding velocity of the water in the model at the same temperature.

Solution

VerifiedAnswered 5 months ago

Answered 5 months ago

Step 1

1 of 2$\textbf{Given:}$

Scale = $\frac{1}{15}$

$V_p = 0.8 \frac{m}{s}$

Since we want to describe similar flows we want the same Reynolds numbers. Also, due to the equal temperature we assume that properties of the water are equal in both flows:

$\begin{align*} Re_p &= Re_m \\\\ \left(\frac{\rho V D}{\mu} \right)_p &= \left(\frac{\rho V D}{\mu} \right)_m\\\\ V_m &= V_p \cdot \frac{D_p}{D_m}\\\\ &= 0.8 \cdot 15 \\\\ &= \boxed{ 12 \; \frac{m}{s}} \end{align*}$

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