#### When fluid flows through pipes there are frictional losses. These losses are due to the resistance due to which some energy of the fluid is lost.

**There are two types of energy loss:**

**Minor loss:** due to friction

**Major loss:** due to sudden expansion or contraction or bend in the pipe.

**Major loss**

It can be calculated with the help of the following formula

**h_f** = Loss of head due to friction

**L** = length of pipe

v = mean velocity of flow

**d** = diameter of the pipe

**f** = coefficient of friction in the viscous flow

**Flow of Viscous fluid through circular pipe**

##### Let us assume a circular cross section pipe of radius R .

##### In the above figure, we have taken a fluid element of radius ‘r’ and length dx.

##### Shear force on the element is given by = τ*(2πr)*dx

##### The pressure at section ab is p then pressure at section cd will be (p+∂p/∂x * dx)

Neglecting the acceleration of fluid element , by balancing net force = 0 , we get

##### Shear Stress distribution as per the above derived equation will be given by

##### By this equation, we can obtain velocity distribution as we know,

**τ = μ du/dy**

But we are measuring y from the surface in the above equation, let’s correlate r & y

### r+y = R

### y = R-r

### dy = 0-dr

### ⇒ **τ = -μ du/dr**

Now, let’s calculate discharge flowing in the small thickness dr

**Discharge dQ = velocity at radius r * Area of the ring**

Average velocity is given by

**u_avg = Q/Area of cross section**