This a dynamics problem how do I solve it A fixed blade is dividing a 3-inch stream of water into two parts. One-quarter (1/4) of the water flows downward, and the remaining three-quarters (3/4) flows upwards. Calculate the horizontal and vertical reactions needed to keep the blade in place, given that the total flow Q is 0.5 cubic feet per second (ft³/s) and the water density (γw) is 62.4 pounds per cubic foot (lb/ft³).**Explanation of Diagram:**The diagram depicts a vertical blade with a stream of water flowing towards it. The stream is shown splitting, with arrows indicating that a portion of the water (1/4) flows downward while the remaining portion (3/4) flows upwards. The blade itself is positioned vertically to redirect the flow of water.

Velocity:v=QA=0.5π43122=10.19fts-1Using momentum equation:dmdt=ρwQ=62.432.20.5=0.9689slugss

A fixed blade is dividing a 3" stream of water in two parts. 1/4 of the water flows downward and the other 3/4 flows upwards. Calculate the horizontal and vertical reactions to keep the blade in place, if the total flow Q = 0.5 ft/s and ľw = 62.4 Ib/ft3.

A fixed blade is dividing a 3" stream of water in two parts. 1/4 of the water flows downward and the other 3/4 flows upwards. Calculate the horizontal and vertical reactions to keep the blade in place, if the total flow Q = 0.5 ft/s and ľw = 62.4 Ib/ft3.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

This a dynamics problem how do I solve it

A fixed blade is dividing a 3-inch stream of water into two parts. One-quarter (1/4) of the water flows downward, and the remaining three-quarters (3/4) flows upwards. Calculate the horizontal and vertical reactions needed to keep the blade in place, given that the total flow Q is 0.5 cubic feet per second (ft³/s) and the water density (γw) is 62.4 pounds per cubic foot (lb/ft³).

**Explanation of Diagram:**
The diagram depicts a vertical blade with a stream of water flowing towards it. The stream is shown splitting, with arrows indicating that a portion of the water (1/4) flows downward while the remaining portion (3/4) flows upwards. The blade itself is positioned vertically to redirect the flow of water.

Expert Solution

Step 1

$V e l o c i t y : v = \frac{Q}{A} = \frac{0.5}{\frac{π}{4} {(\frac{3}{12})}^{2}} = 10.19 f t s^{- 1} U \sin g m o m e n t u m e q u a t i o n : \frac{d m}{d t} = ρ_{w} Q = \frac{62.4}{32.2} (0.5) = 0.9689 \frac{s l u g s}{s}$

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