Hydraulic

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

hydraulic bannerHydraulics is the force or motion applied on a confined liquid.

 

 

 

Hydraulic Conductivity

Hydraulic conductivity ( \(k\) ) is the ease with which a fluid can move through porous spaces or fractures.  See the Darcy's Law.

Hydraulic Diameter

Hydraulic diameter ( \(d_h\) ) is normally used when the flow is in non-circular pipe or tubes and channels.  Circular pipe has the same pressure drop of a rectangular channel but a greater average velocity.  Square or rectangular pipes have a greater weight and a greater pressure drop compared with a circular pipe with the same section.

Hydraulic Diameter FORMULA

\(\large{ d_h = \frac { 4  A } { P  }  }\)         

Where:

\(\large{ d_h }\) = hydraulic diameter

\(\large{ A }\) = cross section area

\(\large{ P }\) = cross section wetting perimeter

Hydraulic Diameter of a tube with a tube on the Insidehydraulic diameter of a pipe in pipe

Hydraulic diameter ( \(d_h\) ) of tube in tube is when the flow is between the inside tube and the outside tube. 

Hydraulic Diameter of a tube with a tube on the Inside FORMULA

\(\large{ d_h =   \frac  { 4     \left( \pi r_{o}{^2}  -  \pi r_{i}{^2}  \right)  }  {  2 \pi r_o  +  2 \pi r_i  }   }\)         

\(\large{ d_h =   \frac  { 4 \pi    \left( r_{o}{^2}  -  r_{i}{^2}  \right)  }  {  2 \pi   \left( r_o  +   r_i \right)  }   }\)         

Where:

\(\large{ d_h }\) = hydraulic diameter

\(\large{ r_i }\) = pipe outside radius of the inside tube

\(\large{ r_o }\) = pipe inside radius of the outside tube

Hydraulic Diameter of an Isosceles Trianglehydraulic diameter of a triangle 3

Hydraulic Diameter of an Isosceles Triangle FORMULA

\(\large{ d_h =  \frac { w\; sin \; \theta   }  {  1 + sin \frac {\theta}{2}  } }\)                

Where:

\(\large{ d_h }\) = hydraulic diameter

\(\large{ w }\) = length of side

\(\large{ \theta }\)   (Greek symbol theta) = degree

 

Hydraulic Diameter of a rectangular Tubehydraulic diameter of a rectangle

Hydraulic diameter ( \(d_h\) ) of a rectangular tube is when the flow is within the tube.

Hydraulic Diameter of a rectangular Tube FORMULA

\(\large{ d_h = \frac  { 4wh } {  2 \left( w + h  \right)  }   }\)          

\(\large{ d_h = \frac  { 2wh } { w + h }   }\)               

Where:

\(\large{ d_h }\) = hydraulic diameter

\(\large{ h }\) = height of tube

\(\large{ w }\) = width of tube

Hydraulic Diameter of a Right Trianglehydraulic diameter of a triangle 2

Hydraulic Diameter of a Right Triangle FORMULA

\(\large{ d_h = \frac  { 2wh } { w + h  +  \left(  w^2 + h^2  \right) ^ \frac{1}{2}   }   }\)                       

Where:

\(\large{ d_h }\) = hydraulic diameter

\(\large{ h }\) = height of tube

\(\large{ w }\) = width of tube

 

Hydraulic Diameter of a Square Tubehydraulic diameter of a square

Hydraulic diameter ( \(d_h\) ) of a square tube is when the flow is within the tube.

Hydraulic Diameter of a Square Tube FORMULA

\(\large{ d_h = w  }\)        

Where:

\(\large{ d_h }\) = hydraulic diameter

\(\large{ w }\) = width of tube

 

Hydraulic Gradienthydraulic gradient

Hydraulic gradient ( \(i\) ) (dimensionless number) is the change in height (pressure) to length.

Hydraulic Gradient FORMULA

\(\large{ i = \frac { h_1 \;-\; h_2} { l}  }\)         

Where:

\(\large{ i }\) = hydraulic gradient

\(\large{ h_1 }\) = pressure head at point 1

\(\large{ h_2 }\) = pressure head at point 2

\(\large{ l }\) = length of column

Solve for:

\(\large{ h_1 = i   l \;+\; h_2  }\)

\(\large{ h_2 = h_1 \;-\; i  l   }\)

\(\large{ l =  \frac { h_1 \;-\; h_2} { i}    }\)

Hydraulic Headhydraulic radius of a triangle

Hydraulic head ( \(h\) ) is the measurement mechanical energy due to pressure of a fluid from a higher elevation to a lower elevation.

Hydraulic Head Formula

\(\large{ h = \frac {p}{g \rho} }\)         

\(\large{ h =  h_1 \;-\; h_2  }\)         

Where:

\(\large{ h }\)= head

\(\large{ g }\) = gravitational acceleration

\(\large{ h_1 }\) = pressure head at point 1

\(\large{ h_2 }\) = pressure head at point 2

\(\large{ p }\) = pressure

\(\large{ \rho }\)   (Greek symbol rho) = density

Hydraulic Radius

Hydraulic radius ( \(r_h\) ) is the cross section area of water in a pipe or channel divided by the wetting perimeter.

Hydraulic Radius formula

\(\large{ r_h =  \frac  {  A }  { P }   }\)         

Where:

\(\large{ r_h }\) = hydraulic radius

\(\large{ A }\) = cross section flow area

\(\large{ P }\) = wetted perimeter

Solve for:

\(\large{ A =  r_h  P  }\)

\(\large{ P = \frac { A } { r_h}  }\)

Hydraulic Radius of a Pipehydraulic radius of a pipe 2

Hydraulic radius ( \(r_h\) ) is the cross section area of water in a pipe or channel divided by the wetting perimeter.

Hydraulic Radius of a Pipe formula

\(\large{ r_h =  \frac  {  A }  { P }   }\)         

\(\large{ r_h =  \frac  {  \frac { d^2  } {  4  \left( \theta  - sin  \;  \left( 2 \theta \right)  \right)  } }  { \theta d }   }\)

\(\large{ r_h =  \frac {d} {4}  \; \frac { 1 - sin \; \left(  2 \theta \right)  }    {  2  \theta  }   }\)

Where:

\(\large{ r_h }\) = hydraulic radius

\(\large{ d }\) = diameter ( \(2r\) )

\(\large{  A }\) = cross section flow area

\(\large{ P }\) = wetted perimeter

\(\large{ \theta }\)   (Greek symbol theta) = degree

Solve for:

\(\large{ \theta = cos^{-1}  \; \left(  1 -  \frac {h} {r}  \right)   }\)

\(\large{ A =   \frac { d^2  } {  4  \left( \theta  - sin  \;  \left( 2 \theta \right)  \right)  }  }\)

\(\large{ P =  \theta d  }\)

Hydraulic Radius of a Rectangular Channelhydraulic radius of a rectangle

Hydraulic radius ( \(r_h\) ) is the cross section area of water in a pipe or channel divided by the wetting perimeter.

Hydraulic Radius of a Rectangular Channel formula

\(\large{ r_h =  \frac  {  A }  { P }   }\)         

\(\large{ r_h =  \frac  {  b h }  { b + 2h }   }\)         

Where:

\(\large{ r_h }\) = hydraulic radius

\(\large{ A }\) = cross section flow area

\(\large{ b }\) = bottom width of fluid

\(\large{ h }\) = depth of fluid

\(\large{ P }\) = wetted perimeter

\(\large{ w }\) = top width of fluid

Solve for:

\(\large{ A =  b h  }\)

\(\large{ P = b + 2h  }\)

Hydraulic Radius of a Trapezoidal Channel (Equal Side Slopes)hydraulic radius of a trapezoid ES

Hydraulic radius ( \(r_h\) ) is the cross section area of water in a pipe or channel divided by the wetting perimeter.

Hydraulic Radius of a Trapezoidal Channel formula

\(\large{ r_h =  \frac  {  A }  { P }   }\)         

\(\large{ r_h =  \frac  {  bh  +  \left( z h \right) 2 }  { b + 2h  \left( bh  +  z h 2  \right)  \frac {1}{2} }   }\)

\(\large{ r_h =  \frac  {  h  \left( b + z h \right) }  { b + 2h  \sqrt { 1 + z^2 }  }   }\)

Where:

\(\large{ r_h }\) = hydraulic radius

\(\large{ A }\) = cross section flow area

\(\large{ b }\) = bottom width of fluid

\(\large{ h }\) = depth of fluid

\(\large{ P }\) = wetted perimeter

\(\large{ w }\) = top width of fluid

\(\large{ z }\) = width of channel slope

Solve for:

\(\large{ A =  bh  +  \left( z h \right) 2  }\)

\(\large{ P = b + 2h  \left( bh  +  z h 2  \right)  \frac {1}{2}  }\)

\(\large{ A =  h  \left( b + z h \right)  }\)

\(\large{ P = b + 2h  \sqrt { 1 + z^2 }  }\)

Hydraulic Radius of a Trapezoidal Channel (Unequal Side Slopes)hydraulic radius of a trapezoid US

Hydraulic radius ( \(r_h\) ) is the cross section area of water in a pipe or channel divided by the wetting perimeter.

Hydraulic Radius of a Trapezoidal Channel formula

\(\large{ r_h =  \frac  {  A }  { P }   }\)         

\(\large{ r_h =  \frac  {  \frac {h^2} {2}  \left( z_1 + x_2 \right) + hg }  { b + h  \left(  \sqrt {  1 + z_{1}{^2}  }  +  \sqrt {  1 + z_{2}{^2}  }   \right) }   }\)

Where:

\(\large{ r_h }\) = hydraulic radius

\(\large{ A }\) = cross section flow area

\(\large{ b }\) = bottom width of fluid

\(\large{ h }\) = depth of fluid

\(\large{ P }\) = wetted perimeter

\(\large{ w }\) = top width of fluid

\(\large{ z }\) = width of channel slope

Solve for:

\(\large{ A =  \frac {h^2} {2}  \left( z_1 + x_2 \right) + hg  }\)

\(\large{ P =  b + h  \left(  \sqrt {  1 + z_{1}{^2}  }  +  \sqrt {  1 + z_{2}{^2}  }   \right)  }\)

 

Tags: Equations for Hydraulic