Question

a horizontal jet of water (at 100c) that is 6 cm in diameter and has a velocity of 20 m/s is deflected by the vane as shown. if the vane is moving at a rate of 7 m/s in the x-direction, what components of force are exerted on the vane by the water in the x- and y-directions? assume negligible friction between the water and the vane.

Answer 1

The net resultant direct force and angle on the vane is created when the water jet exits the vane at position 2 with 92% of its initial velocity.

What is mean by velocity?

• The speed at which a body or object is moving determines its direction of motion. A scalar quantity, speed is primarily. As a matter of fact, velocity is a vector quantity.

• The rate at which distance changes is what it is. It measures the displacement's rate of change. A body's velocity is defined as its speed in a particular direction.

• Velocity is a measure of how quickly a distance changes in relation to time. Having both magnitude and direction, velocity is a vector quantity.

• The rate of change in a body's displacement with respect to time is referred to as velocity. In the SI, m/s is its unit.

Given,

External angle of Curved Vane = 158°

mean velocity at 1 = 12 m/s

Volumetric flow rate = $55 \mathrm{~m}^3 / \mathrm{h}=\frac{55}{3600} \mathrm{~m}^3 / \mathrm{s} .$

mean velocity at $2=12 \times 0.92=11.04 \mathrm{~m} / \mathrm{s}$

i) Force exerted in x - friction A C 1 =  Volume

$F_{S_x} &=\rho A C_1\left[C_2 \cos \theta-C_1\right]$

$&=1000 \times \frac{55}{3600}\left[\left(11.04 \cos 158^{\circ}\right)-12\right]$

i$\rangle F_{\text {sc }}=\supseteq A c_1\left[C_2 \sin \theta\right]$

$&=1000 \times \frac{55}{3600} \times \text { TI. 04 } \sin (1589$

$&F_{\text {syn }}=63.18 \mathrm{~N}$

$&\text { Angle } \Rightarrow \frac{F_{s y}}{F_{3 x}}-\tan \theta$

$&\tan \theta=\frac{63.18}{339.18}, \theta=160-10-5.3$

$&\theta=\tan ^{-}\left(\frac{-63 \cdot 18}{339728}\right)$

$&\theta=-10.540^{\circ}$

The complete question is:

A horizontal jet of water strikes a curved vane as shown in Figure C.1. The external angle of the curved vane is 158°.The mean velocity and volumetric flow rate of the water jet at position 1 are 12 m/s and 55 m³/h respectively. Due to friction, the water jet leaves the vane at position 2 with 92 % its original velocity.

(i) Direct force exerted by the water jet on the vane in the x - direction.

(ii) Direct force exerted by the water jet on the vane in the y - direction.

(ii) Net resultant direct force and angle on the vane.

To learn more about velocity, refer to:

brainly.com/question/24681896

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