Momentum Transfer – Exam

Hydrogen is pumped from a reservoir of 2 MN/m² pressure through a clean horizontal
mild steel pipe, 50 mm diameter and 500 m long. The downstream pressure is also
2MN/m² and the pressure of the gas is raised to 2.6 MN/m² by a pump at the upstream
end of the pipe. The conditions of flow are isothermal, and the temperature of the gas is
293K. The efficiency of the pump is 0.6 and the viscosity of hydrogen is 0.009 mNs/m² at
293 K. What is the effective rate of working in the pump?

De Laval nozzles are famously called as

Two tanks, the bottoms of which are at the same level, are connected with one another by
a horizontal pipe 75 mm diameter and 300 m long. The pipe is bell-mouthed at each end
so that losses on entry and exit are negligible. One tank is 7 m diameter and contains
water to a depth of 7 m. The other tank is 5 m diameter and contains water to a depth of 3
m. If the tanks are connected to each other by means of the pipe, how long will it take
before the water level in the larger tank has fallen to 6 m? Assume the pipe to be of aged
mild steel, roughness is 0.05 mm.

A150 mm gas main is used for transferring gas (MW = 13 kg/kmol and velocity = 0.25
cm²/s at 295 K from a plant to a storage station 100 m away, at a rate of 1 m³/s. If the
maximum permissible pressure drop is 10 kN/m², is it possible to increase the flow rate
by 25%?

A Venturi meter is to be installed in a 100 mm line to measure the flow of water. The
maximum flow rate is expected to be 75 m3/h at 15 deg C. The manometer used to
measure the differential pressure is to be filled with mercury and water is to fill the leads
above the surfaces of the mercury. The water temperature will be 15 deg C. throughout.
What will be the power to operate the meter at full load if the pressure recovery is 90% of
the differential pressure?

The volume remaining in the cylinder after the forward stroke of the piston.

A gas, having a molecular weight of 13 kg/kmol and a kinematic viscosity of 0.25 cm²/s
flows through a pipe 0.25 m internal diameter and 5 km long at the rate of 0.4 m³/s and is
delivered at atmospheric pressure. The volume occupied by 1 kmol at 273 K and 101.3
kN/m² is 22.4 m³. What would be the effect on the required pressure if the gas were to be
delivered at a height of 150m below its point of entry into the pipe?

Over a limited range of shear rate, dilatants may be fit to the power model with:

In multiphase horizontal flow, the liquid flows along the bottom of the pipe, and the gas
flows over a smooth liquid/gas interphase during:

A cube measuring 1 ft on a side is submerged so that its top face is 10 ft below the free
surface of water. Determine the magnitude and direction of the applied force necessary to
hold the cube in this position if it is made of Steel with a density of 490 lb/ft³.

Find the drop in pressure due to friction in a glazed porcelain pipe 300 m long and 150
mm diameter when water is flowing at the rate of 0.05 m³/s.

These are curves on which are found all the material particles that passed through a
particular point in space at some earlier time.

A petroleum product of viscosity 0.5 m Ns/m² and density 700 kg/m³ is pumped through
a pipe of 0.15 m diameter to storage tanks situated 100 m away. The pressure drop along
the pipe is 70 kN/m². The pipeline has to be repaired and it is necessary to pump the
liquid by an alternative route consisting of 70 m of 200 mm pipe followed by 50 m of 100
mm pipe. Take the roughness of the pipe surface as 0.05 mm. If the existing pump is
capable of developing a pressure of 300 kN/m², will it be suitable for use during the
period required for the repairs?

A gas, having a molecular weight of 13 kg/kmol and a kinematic viscosity of 0.25 cm²/s,
flows through a pipe 0.25 m internal diameter and 5 km long at the rate of 0.4 m³/s and is
delivered at atmospheric pressure. The volume occupied by 1 kmol at 273 K and 101.3
kN/m² is 22.4 m³. What would be the effect on the required pressure if the gas were to be
delivered at a height of 150 m below its point of entry into the pipe?

A venturi meter with a 50 mm throat is used to measure a flow of slightly salt water in a
pipe of inside diameter 100 mm. The meter is checked by adding 20 cm³/s of normal
sodium chloride solution above the meter and analysing a sample of water downstream
from the meter. Before addition of the salt, 1000 cm³ of water requires 10 cm3 of 0.1 M
silver nitrate solution in a titration. 1000 cm3 of the downstream sample required 23.5
cm³ of 0.1 M silver nitrate. The mercury-under-water manometer connected to the meter
gives a reading of 221 mm. Assume that the density of the liquid is not appreciably
affected by the salt.What is the discharge coefficient of the meter?

Water flowing at 1.5 l/s in a 50 mm diameter pipe is metered by means of a simple orifice
of diameter 25 mm. The coefficient of discharge of the meter is 0.62 and the Viscosity of
water = 1 mN s/m². What will be the reading on a mercury-under-water manometer
connected to the meter?

A gas cylinder containing air discharges to atmosphere through a valve whose
characteristics may be considered similar to those of a sharp-edged orifice. The pressure
in the cylinder is initially 350 kN/m2. The flow through the valve may be taken as
isentropic and the expansion in the cylinder as isothermal. The ratio of the specific heats
at constant pressure and constant volume is 1.4. By how much will the pressure have
fallen when the flowrate has decreased to one-quarter of its initial value?

If a pitot tube is inserted in a circular cross-section pipe in which a fluid is in streamline
flow, calculate at what point in the cross-section it should be situated so as to give a
direct reading representative of the mean velocity of flow of the fluid.

The differential equation for conservation of momentum is called

A single-stage double-acting compressor running at 3 Hz is used to compress air from
110 kN/m² and 282 K to 1150 kN/m². If the internal diameter of the cylinder is 20 cm,
the length of stroke 25 cm, and the piston clearance 5%, calculate the theoretical power
requirements under isentropic conditions.

There are smooth streamlines and the fluid velocity components vary smoothly with
position and time.

Refers to the rate of viscous energy dissipation to internal energy.

Occurs in stirred tanks where fluid elements entering the tank at different times are
intermingled.

Methane is to be compressed from atmospheric pressure to 30 MN/m² in four stages.
Assume compression to be isentropic and the gas to behave as an ideal gas. Indicate on a
temperature–entropy diagram the effect of imperfect intercooling on the work done at
each stage. Calculate the work required per kilogram of gas.

Fluids which the slope of the rheogram decreases with increasing shear rate.

If the temperature rise per meter length along a pipe carrying air at 12.2 m/s is 66 deg K,
what will be the corresponding pressure drop for a pipe temperature of 420 K and an air
temperature of 310 K? The density of air at 310 K is 1.14 kg/m³.

The ratio of shear stress to shear rate.

What is needed to completely describe the stress rate for microscopic momentum
balances in multidimensional flow?

Under molecular flow conditions, what is the relationship of conductance and pressure?

Water leaves the 25 mm diameter nozzle of a fire hose at a velocity of 25 m/s. What will
be the reaction force at the nozzle which the fireman will need to counterbalance?

Ninety-eight per cent sulphuric acid is pumped at 4.5 tonne/h (1.25 kg/s) through a 25
mm diameter pipe, 30 m long, to a reservoir 12 m higher than the feed point. Calculate
the pressure drop in the pipeline.

On the assumption that the velocity profile in a fluid in turbulent flow is given by the
Prandtl one-seventh power law, calculate the radius at which the flow between it and the
centre is equal to that between it and the wall, for a pipe 100 mm in diameter.

Water flows at 7.2 m³/h through a sudden enlargement from 40 mm to 50 mm diameter
pipe. What is the loss in head?

As the fluid moves towards the Vienna contracta, it is _____ and pressure energy is
convert into _______.

This defines the relations between shear stress and shear rate for Newtonian Fluid.

This refers to the ability to store and recover shear energy and therefore show some of the
properties of both a solid and aliquid.

A Newtonian liquid of viscosity 0.1 N s/m2 is flowing through a pipe of 25 mm diameter
and 20 m in length, and the pressure drop is 105 N/m2. As a result of a process change a
small quantity of polymer is added to the liquid and this causes the liquid to exhibit non-
Newtonian characteristics; its rheology is described adequately by the power-law model
and me flow index is 0.33. The apparent viscosity of the modified fluid is equal to the
viscosity of the original liquid at a shear rate of 1000 s~’. If the pressure difference over
the pipe is unaltered, what will be the ratio of the volumetric flowrates of the two liquids?

What is the surface roughness of wrought iron in mm?

This refers to the transportation of solid particles in liquids.

Which among the following is true about flow of coarse solids: