Variation of Pressure in a Fluid

Consider a small fluid element of size δx × δy × δz at any point in a static mass of fluid as shown in Fig.1. Since the fluid is at rest, the element is in equilibrium under the various forces acting on it. The forces acting on the element are the pressure forces on its faces and the self-weight of the element.

Let ‘p’ be the pressure intensity at the midpoint O of the element. Then the pressure intensity on the left hand face of the element is

The pressure intensity on the right hand face of the element is 

The corresponding pressure forces on the left hand and the right hand faces of the element are

 and

 respectively.

Fig. 1 Fluid Element with Forces Acting on it in a Static Mass of Fluid

Likewise the pressure intensities and the corresponding pressure forces on the other faces of the element may be obtained as shown in Fig. 1. Further if ‘w’ is the specific weight of the fluid then the weight of the element acting vertically downwards is (w δx δy δz). Since the element is in equilibrium under these forces, the algebraic sum of the forces acting on it in any direction must be zero. Thus considering the forces acting on the element along x,y and z axes the following equations are obtained

                                 ΣFx = 0

                        or                                                     ΣFy = 0

                               or                                               ΣFz = 0

Equations 1, 2 and 3 indicate that the pressure intensity p at any point in a static mass of fluid does not vary in x and y directions and it varies only in z direction. Hence the partial derivative in eq. 3 may be reduced to total (or exact) derivative as follows.

In vector notation Eq. 4 may be expressed as

– grad p = wk = ρgk

where ‘k’ is unit vector parallel to z axis.

The minus sign (–) in the above equation signifies that the pressure decreases in the direction in which z increases i.e., in the upward direction.

Equation 4 is the basic differential equation representing the variation of pressure in a fluid at rest, which holds for both compressible and incompressible fluids. Equation 4 indicates that within a body of fluid at rest the pressure increases in the downward direction at the rate equivalent to the specific weight ‘w’ of the liquid. Further if dz = 0, then dp is also equal to zero; which means that the pressure remains constant over any horizontal plane in a fluid.

Read More

Road Margins

The portion of the road beyond the carriageway and on the roadway can be generally called road margin. Various elements that form the road margins are given below.

1) Shoulders

Shoulders are provided along the road edge and are intended for accommodation of stopped vehicles, serve as an emergency lane for vehicles and provide lateral support for base and surface courses. The shoulder should be strong enough to bear the weight of a fully loaded truck even in wet conditions. The shoulder width should be adequate for giving working space around a stopped vehicle. It is desirable to have a width of 4.6 m for the shoulders. A minimum width of 2.5 m is recommended for 2- lane rural highways in India.

2) Parking Lanes

Parking lanes are provided in urban lanes for side parking. Parallel parking is preferred because it is safe for the vehicles moving on the road. The parking lane should have a minimum of 3.0 m width in the case of parallel parking.

3) Bus-bays

Bus bays are provided by recessing the kerbs for bus stops. They are provided so that they do not obstruct the movement of vehicles in the carriage way. They should be at least 75 meters away from the intersection so that the traffic near the intersections is not affected by the bus-bay.

4) Service Roads

Service roads or frontage roads give access to access controlled highways like freeways and expressways. They run parallel to the highway and will be usually isolated by a separator and access to the highway will be provided only at selected points. These roads are provided to avoid congestion in the expressways and also the speed of the traffic in those lanes is not reduced.

5) Cycle Track

Cycle tracks are provided in urban areas when the volume of cycle traffic is high. Minimum width of 2 m is required, which may be increased by 1 m for every additional track.

6) Footpath

Footpaths are exclusive right of way to pedestrians, especially in urban areas. They are provided for the safety of the pedestrians when both the pedestrian traffic and vehicular traffic is high. Minimum width is 1.5 m and may be increased based on the traffic. The footpath should be either as smooth as the pavement or smoother than that to induce the pedestrian to use the footpath.

7) Guard rails

They are provided at the edge of the shoulder usually when the road is on an embankment. They serve to prevent the vehicles from running off the embankment, especially when the height of the fill exceeds 3 m. Various designs of guard rails are there. Guard stones painted in alternate black and white are usually used. They also give better visibility of curves at night under headlights of vehicles.

Read More

Kerbs in Pavement

Kerbs indicate the boundary between the carriage way and the shoulder or islands or footpaths. The different types of kerbs are given below.

1) Low or Mountable Kerbs

This type of kerb is provided such that they encourage the traffic to remain in the through traffic lanes and also allow the driver to enter the shoulder area with little difficulty. These kerbs are indicator between the boundary of a road and shoulder. The height of this kerb is about 10 cm above the pavement edge with a slope which allows the vehicle to climb easily. This is usually provided at medians and channelization schemes and also helps in longitudinal drainage.

Fig. 1 Low or Mountable Kerb

2) Semi-Barrier Type Kerbs

When the pedestrian traffic is high, these kerbs are provided. Their height is 15 cm above the pavement edge. This type of kerb prevents encroachment of parking vehicles, but at acute emergency it is possible to drive over this kerb with some difficulty.

Fig. 2 Semi-Barrier Type Kerb

3) Barrier Type Kerbs

They are designed to discourage vehicles from leaving the pavement. They are provided when there is considerable amount of pedestrian traffic. They are placed at a height of 20 cm above the pavement edge with a steep batter. Generally, its height is 23 to 45cm and such kerbs are provided on hills, bridges etc.

Fig. 3 Barrier Type Kerb

4) Submerged Kerbs

They are used in rural roads. The kerbs are provided at pavement edges between the pavement edge and shoulders. They provide lateral confinement and stability to the pavement.

Fig. 4 Submerged Kerb 

Read More

Width of Carriage Way, Width of Formation and Right of Way

Width of Carriage Way

Width of the carriage way or the width of the pavement depends on the width of the traffic lane and number of lanes. Width of a traffic lane depends on the width of the vehicle and the clearance. Side clearance improves operating speed and safety. The maximum permissible width of a vehicle is 2.44 m and the desirable side clearance for single lane traffic is 0.68 m. This require minimum of lane width of 3.75 m for a single lane road (Fig.1). However, the side clearance required is about 0.53 m, on either side and 1.06 m in the center. Therefore, a two lane road require minimum of 3.5 meter for each lane (Fig.1). The desirable carriage way width recommended by IRC is given in Table 1.

Fig. 1 Lane Width of Single and Two Lane Roads

Table 1 IRC Specification for Carriage Way Width

Type of Carriage Way	Width (m)
Single lane	3.75
Two lane, no kerbs	7.0
Two lane, raised kerbs	7.5
Intermediate carriage	5.5
Multi-lane	3.5

Fig. 2 Representation of Various Road Width

Width of Formation/Roadway Width

Width of formation or roadway width is the sum of the widths of pavements or carriage way including separators and shoulders. This does not include the extra land in formation/cutting. The values suggested by IRC are given in Table 2.

Table 2 Width of Formation of Various Classification of Roads

Road Classification	Roadway width in m
	Plain and Rolling Terrain	Mountainous and Steep Terrain
NH/SH	12	6.25 - 8.8
MDR	9	4.75
ODR	7.5 - 9.0	4.75
VR	7.5	4.0

Right of Way/ Land Width

Right of way (RoW) or land width is the width of land acquired for the road, along its alignment. It should be adequate to accommodate all the cross-sectional elements of the highway and may reasonably provide for future development. To prevent ribbon development along highways, control lines and building lines may be provided. Control line is a line which represents the nearest limits of future uncontrolled building activity in relation to a road. Building line represents a line on either side of the road, between which and the road no building activity is permitted at all. The right of way width is governed by:

• Width of formation : It depends on the category of the highway and width of roadway and road margins.
• Height of embankment or depth of cutting : It is governed by the topography and the vertical alignment.
• Side slopes of embankment or cutting : It depends on the height of the slope, soil type etc.
• Drainage system and their size which depends on rainfall, topography etc.
• Sight distance considerations : On curves etc. there is restriction to the visibility on the inner side of the curve due to the presence of some obstructions like building structures etc.
• Reserve land for future widening : Some land has to be acquired in advance anticipating future developments like widening of the road.

The importance of reserved land is emphasized by the following. Extra width of land is available for the construction of roadside facilities. Land acquisition is not possible later, because the land may be occupied for various other purposes (buildings, business etc.) The normal RoW requirements for built up and open areas as specified by IRC is given in Table 3.

Table 3 Normal Right of Way for Open Areas

Road Classification	Roadway width in m
	Plain and Rolling Terrain	Mountainous and Steep Terrain
Open Areas
NH/SH	45	24
MDR	25	18
ODR	15	15
VR	12	9
Built-up Areas
NH/SH	30	20
MDR	20	15
ODR	15	12
VR	10	9

Read More