Jawaharlal Nehru Technological University Hyderabad
Jawaharlal Nehru Technological University Hyderabad B.Tech II FLUID MECHANICS Previous Question Paper (August/ September - 2022 - R15)
Answer any five questions. All questions carry equal marks.
Main
Show that the rate of increase of pressure in a vertical downward direction when fluid at rest is equal to the weight density of the fluid at that point.
Answer
Consider a small fluid element of cross-sectional area dA and height dz at a depth z from the free surface. The forces acting on the element in the vertical direction are: 1. Pressure force acting downwards on the top face: P × dA. 2. Pressure force acting upwards on the bottom face: (P + dP) × dA. 3. Weight of the fluid element acting downwards: W = ρ × g × dA × dz. For the fluid to be in equilibrium, the net vertical force must be zero:
Simplifying this expression:
Since ρ × g is the weight density (w) of the fluid, the rate of increase of pressure in the downward direction (dz) is equal to the weight density of the fluid.
Derive an expression for the depth of Centre of pressure from free surface of liquid of an inclined plane surface sub-merged in the liquid.
Answer
Consider an inclined plane surface submerged in a liquid at an angle θ with the free surface. Let A be the total area, G be the centroid, and P be the centre of pressure. Let h_bar be the depth of the centroid and h* be the depth of the centre of pressure. The pressure force on an elemental area dA at a distance y from the axis of rotation (O) is dF = ρ × g × (y sinθ) × dA. The moment of this force about O is dM = dF × y = ρ × g × sinθ × y^2 × dA. The total moment M = ∫ dM = ρ × g × sinθ × ∫ y^2 × dA. Since ∫ y^2 × dA = I_O (moment of inertia about O), M = ρ × g × sinθ × I_O. The moment of the total force F = ρ × g × A × h_bar about O is also equal to F × y* = (ρ × g × A × h_bar) × y*, where y* is the distance of the centre of pressure from O. Equating the two moments:
Using the parallel axis theorem I_O = I_G + A × y_bar^2, where y_bar = h_bar / sinθ:
Multiplying by sinθ to convert to vertical depth h* = y* sinθ:
Explain with sketch, how an inverted U-tube manometer is used to measure small pressure differences.
Answer
Sign in to view the complete answer paper.
A flat plate weighing 0.65 KN has a surface area of 0.25 m2. It slides down an inclined plane at 350 to the horizontal at a constant speed of 4 m/s. If the inclined plane is lubricated with an oil of viscosity 0.18 N-s/m2. Find the thickness of the oil film.
Answer
Sign in to view the complete answer paper.
What is flow net? What are advantages and limitations of flow net analysis?
Answer
Sign in to view the complete answer paper.
The water is flowing through a taper pipe of length 120m having diameters 630 mm at the upper end and 320mm at the lower end at the rate of 55 lit/s. The pipe has a slope of 1 in 30. Find the pressure at the lower end if the pressure at the higher level is 21.62 N/cm2.
Answer
Sign in to view the complete answer paper.
Explain continuity equation and derive the continuity equation for one dimensional flow.
Answer
Sign in to view the complete answer paper.
The stream function for a two-dimensional flow is given by ψ = 3xy. Calculate the velocity at the point P (3, 4). Find the velocity potential function φ.
Answer
Sign in to view the complete answer paper.
Derive an expression for the maximum discharge over a broad crested weir.
Answer
Sign in to view the complete answer paper.
A pipe bend tapers from a diameter of 530mm at inlet to a diameter of 280 mm at outlet and the flow is turned through 770. The pressures at inlet and outlet are 4.5 N/m2 and 3.5 N/m2. If the pipe is converging oil of specific gravity 0.88, calculate the magnitude and direction of the resultant force on the bend when the oil flow rate is 0.55 m3/s. The bend is in a horizontal plane.
Answer
Sign in to view the complete answer paper.
What is pitot tube? How is it used to measure velocity of flow at any point in a pipe.
Answer
Sign in to view the complete answer paper.
A horizontal venturimeter with inlet and throat diameters 42 cms and 25 cms respectively is used to measure the flow of water. The reading of differential Manometer connected to the inlet and throat is 20 cm of mercury. Determine the rate of flow. Take Cd=0.97.
Answer
Sign in to view the complete answer paper.
Explain laminar boundary layer over a thin flat plate in detail.
Answer
Sign in to view the complete answer paper.
Derive Von Karman momentum integral equation in detail.
Answer
Sign in to view the complete answer paper.
Show that the loss of head due to sudden expansion in a pipeline is a function of velocity head.
Answer
Sign in to view the complete answer paper.
A liquid of viscosity 0.21 N-s/m2 and specific gravity 0.85 is filled between two horizontal plates 10 mm apart. If the upper plate is moving at 2 m/s and the pressure difference between two sections 10 m apart is 9.81 kN/m2. Determine the shear stress on the plate.
Answer
Sign in to view the complete answer paper.