Solve the Problem $\mathbf { F }$ Of a Fluid Has a Constant Magnitude

question 204

Essay

Solve the problem.
-The velocity field $\mathbf { F }$ of a fluid has a constant magnitude $\mathrm { k }$ and always points towards the origin. Following the smooth curve $y = f ( x )$ from $( a , f ( a ) )$ to $( b , f ( b ) )$ , show that the flow along the curve is
$$\int _ { C } \mathbf { F } \cdot \mathbf { T } d s = k \left[ \left( a ^ { 2 } + ( f ( a ) ) ^ { 2 } \right) ^ { 1 / 2 } - \left( b ^ { 2 } + ( f ( b ) ) ^ { 2 } \right) ^ { 1 / 2 } \right]$$

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Definitions:

Cost of Goods Sold

The immediate expenses related to creating a company's sold products, encompassing the price of materials and the labor specifically involved in manufacturing the item.

Gross Profit Inventory Method

An accounting method to estimate the value of ending inventory and cost of goods sold using the gross profit margin.

Inventory Valuation

The method used to determine the cost associated with an inventory at the end of an accounting period, impacting the cost of goods sold and net income.

Gross Profit

The financial metric indicating the difference between revenue and the cost of goods sold (COGS), reflecting the efficiency of core operations.